Tribology of Metal Cutting, Volume 52 (Tribology and Interface Engineering)

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TRIBOLOGY OF METAL CUTTING

TRIBOLOGY AND INTERFACE ENGINEERING SERIES Editor B.J. Briscoe (U.K.) Advisory Board M.J. Adams (U.K.) J.H. Beynon (U.K.) D.V. Boger (Australia) P. Cann (U.K.) K. Friedrich (Germany) I.M. Hutchings (U.K.)

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Vol. 37 Vol. 38 Vol. 39 Vol. Vol. Vol. Vol. Vol. Vol. Vol. Vol. Vol. Vol. Vol.

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J. Israelachvili (U.S.A.) S. Jahanmir (U.S.A.) A.A. Lubrecht (France) I.L Singer (U.S.A.) G.W. Stachowiak (Australia)

Dissipative Processes in Tribology (Dowson et al., Editors) Coatings Tribology – Properties, Techniques and Applications in Surface Engineering (Holmberg and Matthews) Friction Surface Phenomena (Shpenkov) Lubricants and Lubrication (Dowson et al., Editors) The Third Body Concept: Interpretation of Tribological Phenomena (Dowson et al., Editors) Elastohydrodynamics – ’96: Fundamentals and Applications in Lubrication and Traction (Dowson et al., Editors) Hydrodynamic Lubrication – Bearings and Thrust Bearings (Frêne et al.) Tribology for Energy Conservation (Dowson et al., Editors) Molybdenum Disulphide Lubrication (Lansdown) Lubrication at the Frontier – The Role of the Interface and Surface Layers in the Thin Film and Boundary Regime (Dowson et al., Editors) Multilevel Methods in Lubrication (Venner and Lubrecht) Thinning Films and Tribological Interfaces (Dowson et al., Editors) Tribological Research: From Model Experiment to Industrial Problem (Dalmaz et al., Editors) Boundary and Mixed Lubrication: Science and Applications (Dowson et al., Editors) Tribological Research and Design for Engineering Systems (Dowson et al., Editors) Lubricated Wear – Science and Technology (Sethuramiah) Transient Processes in Tribology (Lubrecht, Editor) Experimental Methods in Tribology (Stachowiak and Batchelor) Tribochemistry of Lubricating Oils (Pawlak) An Intelligent System For Tribological Design In Engines (Zhang and Gui) Tribology of Elastomers (Si-Wei Zhang) Life Cycle Tribology (Dowson et al., Editors) Tribology in Electrical Environments (Briscoe, Editor) Tribology & Biophysics of Artificial Joints (Pinchuk)

Aims & Scope The Tribology Book Series is well established as a major and seminal archival source for definitive books on the subject of classical tribology. The scope of the Series has been widened to include other facets of the now-recognised and expanding topic of Interface Engineering. The expanded content will now include: • colloid and multiphase systems; • rheology; • colloids; • tribology and erosion; • processing systems; • machining; • interfaces and adhesion; as well as the classical tribology content which will continue to include • friction; contact damage; • lubrication; and • wear at all length scales.

TRIBOLOGY AND INTERFACE ENGINEERING SERIES, 52 EDITOR: B.J. BRISCOE

TRIBOLOGY OF METAL CUTTING VIKTOR P. ASTAKHOV

Amsterdam – Boston – Heidelberg – London – New York – Oxford Paris – San Diego – San Francisco – Singapore – Sydney – Tokyo

Elsevier Elsevier Elsevier Elsevier

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© 2006 Elsevier Ltd. All rights reserved. This work is protected under copyright by Elsevier Ltd, and the following terms and conditions apply to its use: Photocopying Single photocopies of single chapters may be made for personal use as allowed by national copyright laws. Permission of the Publisher and payment of a fee is required for all other photocopying, including multiple or systematic copying, copying for advertising or promotional purposes, resale, and all forms of document delivery. Special rates are available for educational institutions that wish to make photocopies for non-profit educational classroom use. Permissions may be sought directly from Elsevier’s Rights Department in Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; e-mail: [email protected]. Requests may also be completed on-line via the Elsevier homepage (http://www.elsevier.com/locate/permissions). In the USA, users may clear permissions and make payments through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA; phone: (+1) (978) 7508400, fax: (+1) (978) 7504744, and in the UK through the Copyright Licensing Agency Rapid Clearance Service (CLARCS), 90 Tottenham Court Road, London W1P 0LP, UK; phone: (+44) 20 7631 5555; fax: (+44) 20 7631 5500. Other countries may have a local reprographic rights agency for payments. Derivative Works Tables of contents may be reproduced for internal circulation, but permission of the Publisher is required for external resale or distribution of such material. Permission of the Publisher is required for all other derivative works, including compilations and translations. Electronic Storage or Usage Permission of the Publisher is required to store or use electronically any material contained in this work, including any chapter or part of a chapter. Except as outlined above, no part of this work may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior written permission of the Publisher. Address permissions requests to: Elsevier’s Rights Department, at the fax and e-mail addresses noted above. Notice No responsibility is assumed by the Publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made. First edition 2006 ISBN–13: 978-0-444-52881-0 ISBN–10: 0-444-52881-4 ISSN: 1572-3364 (series) The paper used in this publication meets the requirements of ANSI/NISO Z39.48-1992 (Permanence of Paper). Printed in Great Britain 06 07 08 09 10

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CONTENTS

PREFACE

ix

1.

GENERALIZED MODEL OF CHIP FORMATION

1

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10

Introduction Inadequacy of the Single-Shear Plane Model What is the Model of Chip Formation? System Concept in Metal Cutting Generalized Model of Chip Formation Influence of Cutting Speed Formation of Saw-Toothed Chip Frequency of Chip Formation Formation of the Segmental Saw-Toothed Chip Applicability and Significance of Chip Formation Models References

1 2 21 23 23 43 48 53 55 60 62

2.

ENERGY PARTITION IN THE CUTTING SYSTEM

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2.1 2.2 2.3 2.4

Introduction Energy Flows in the Cutting System Physical Efficiency of the Cutting System Determination of the Work of Plastic Deformation in Metal Cutting Practical Analysis of the Physical Efficiency of the Cutting System Energy Balance of the Cutting System

69 70 73

2.5 2.6

76 91 94

vi 2.7

Contents Methods of Improving Physical Efficiency of the Cutting System References

98 120

TRIBOLOGY OF THE TOOL–CHIP AND TOOL–WORKPIECE INTERFACES

124

3.1 3.2 3.3 3.4

Introduction Tool–Chip Interface Tool–Workpiece Interface Temperature at the Interfaces References

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4.

CUTTING TOOL WEAR, TOOL LIFE AND CUTTING TOOL PHYSICAL RESOURCE

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4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9

Introduction Known Approaches Proper Assessment of Tool Wear Optimal Cutting Temperature – The First Metal Cutting Law Influence of Cutting Feed and Depth of Cut Influence of Tool Geometry Influence of Workpiece Diameter Plastic Lowering of the Cutting Edge Resource of the Cutting Wedge References

220 221 224 227 239 245 248 254 269 274

5.

DESIGN OF EXPERIMENTS IN METAL CUTTING TESTS

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5.1 5.2 5.3 5.4 5.5

Introduction DOE in Machining: Terminology and Requirements Screening Test 2k Factorial Experiment, Complete Block Group Method of Data Handling References

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IMPROVEMENTS OF TRIBOLOGICAL CONDITIONS

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6.1 6.2 6.3

Cutting Fluids (Coolants) Coatings Improving Tribological Conditions by Modification of Properties of the Work Material References

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3.

379 386

Contents

APPENDIX A A1 A2 A3 A4

Basic Terms and Definitions Reference Planes Angles: Definitions Determination of Uncut Chip Thickness for a General Case References

APPENDIX B B1 B2

BASICS, DEFINITIONS AND CUTTING TOOL GEOMETRY

EXPERIMENTAL DETERMINATION OF THE CHIP COMPRESSION RATIO (CCR)

General Experimental Techniques Design of Experiment

INDEX

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PREFACE

This book is about a subject that has been lurking in the underbrush of the manufacturing world for many years and is finally coming to the forefront. Tribology of metal cutting is, in some ways, the ugly beast that content providers – metal cutting researchers, tool and machine tool companies, market researchers and sales personnel, major manufacturing corporations and others – have wanted to keep in the closet. Global competition has forced the closet door open; really, it has eliminated the door itself. What used to be relatively simple and written as a set of postulates in texts on the subject is now uncomfortably complex. Historical Background The term tribology comes from the Greek word tribos, meaning friction, and logos, meaning law. Tribology is therefore defined as “the science and technology of interactive surfaces moving in relation to each other.” The science of Tribology concentrates on contact physics and the mechanics of moving interfaces that generally involve energy dissipation. Its findings are primarily applicable in mechanical engineering and design where tribological interfaces are used to transmit, distribute and/or convert energy. The contact between two materials, and the friction that one exercises on the other, causes an inevitable process of wear. What those contact conditions are, how to strengthen the resistance of contact surfaces to the resulting wear, as well as optimizing the power transmitted by mechanical systems and complex lubrication they require, have become a specialized applied science and technical discipline which has seen major growth in recent decades. Bearing the rather colorful name “Applied tribology,” this field of research and application encompasses the scientific fields of contact mechanics, kinematics, applied physics, surface topology, hydro- and thermodynamics, and many other engineering fields under a common umbrella, related to a great variety of physical and chemical processes and reactions that occur at tribological interfaces. When it comes to metal cutting, tribology is thought of as something that has to be studied in order to reduce the tool wear (and thus increase tool life). Although this is true

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in general, it does not exhaust the application of tribological knowledge in metal cutting. Unfortunately, the published books and articles on the subject do not treat the subject in a systematic way. Rather, the collection of non-correlated facts on tool materials, cutting regimes, tool life and its assessment, cutting fluids, tool coatings, etc., is considered as the tribology of metal cutting. Having read the known works and related materials, one does not feel thoroughly equipped to analyze and improve the tribological conditions in various metal cutting operations. This is because of the commonly understood meaning of “metal cutting tribology,” which is something related to reduction of tool wear, its assessment and reduction. Although it is true that cutting tool wear and its proper assessment is a part of metal cutting tribology, the assessment and reduction of tool wear are only “natural by-products” of this field of study. To proceed further and to comprehend the content of this book properly, one should clearly realize that the ultimate objective of metal cutting tribology is the reduction in the energy spent in metal cutting. Increased tool life, improved integrity of the machined surface, higher process efficiency and stability are the results of achieving this goal. This book attempts to provide specialists in the field of metal cutting with information on how to apply the major ideas of metal cutting tribology, or, in other words, how to make metal cutting tribology useful at various levels (starting with tool design, developing and/or selecting proper tool materials including coating, development and/or selecting proper cutting fluids and ending with cutting process optimization on the shop floor).

The Importance of the Subject Although in the practice of mechanical engineering, the waste of resources (energy) due to ignorance of tribological effects hardly exceeds a single digit, this waste is estimated to be approximately one-third of the world’s energy consumption, so the study and optimization of tribological process are considered to be of great importance. Enormous sums of money are spent on research in tribology. The objective of this research is understandably the minimization and elimination of losses resulting from friction and wear at all levels of technology where rubbing of surfaces is involved. It is claimed, research in tribology leads to greater plant efficiency, better performance, fewer breakdowns and significant savings. In metal cutting, only 30–50% of the energy required by the cutting system is spent for the useful work, i.e. for the separation of the layer from the workpiece, as is conclusively proven in this book. This means that 25–60% of the energy consumed by the cutting system is simply wasted. Most of this wasted energy is spent at the tool–chip and tool– workpiece interfaces due to unoptimized tribological processes. This fact can be easily appreciated if one realizes that nearly all the energy spent in the cutting process is converted into thermal energy. Therefore, the temperature of a certain zone in the cutting system is a relevant indicator of the energy spent in this zone. This is because the energy spent generates heat, thus the higher temperature of a particular zone indicates greater energy spent in this zone. If we compare the temperature in the deformation zone and that at the discussed interfaces, we can come to a surprising yet well-known conclusion that the temperature in the deformation zone, where the major work of plastic deformation

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and separation of the layer being removed from the rest of the workpiece takes place, is relatively low (normally in the range of 80–250◦ C), while the maximum temperatures at the tool–chip interface exceeded 1000◦ C. Therefore, most of the energy required by the cutting system is spent at the tool–chip and tool–workpiece interfaces. Unfortunately, this simple fact has been overlooked for years, so the deformation zone attracts much more attention from researchers in the field with less attention to the tribological aspects of metal cutting. Naturally, this energy spent at the discussed interfaces lowers tool life, affects the shape of the produced chip, and leads to the necessity of using different cooling media that, in turn, lowers the efficiency of the machining system as more energy is needed for cooling medium delivery and maintenance. The situation in metal cutting is entirely different from that in the design of tribological joints in modern machinery. In the latter, a designer is rather limited by the shape of the contacting surfaces, materials used, working conditions set by the outside operating requirements, use of cooling and lubricating media, etc. In metal cutting, practically any parameters of the cutting system can be varied in a wide range. Modern machine tools do not limit a process designer in his selection of cutting speeds, feeds or depth of cut. The nomenclatures of tool materials, geometries of cutting inserts and tool holders available at his disposal are very wide. The selection of cooling and lubrication media, and their application techniques are practically unlimited. Although the chemical composition of the work material is normally given as set by the designer, the properties of this material can be altered over a wide range by heat treatment, forging and casting conditions. The only problem in the selection of optimal tribological cutting parameters is the lack of knowledge on the metal cutting tribology. Therefore, study and optimization of the tribological conditions at these interfaces have a great potential in terms of reduction of the energy spent in cutting, increased tool life, reduction and elimination of coolants, etc. The optimization of tribological processes in metal cutting results in the following: • Reduction of the energy spent in cutting. Because the efficiency of the cutting system is very low (in machining of most steels it does not exceed 50%) due to energy losses during tribological interactions, the optimization of the tribological processes improves the efficiency of the cutting system by reducing the energy spent by the cutting system. • Proper selection of application-specific tool material (coating). Considering the energy transmitted through the tribological interfaces in metal cutting, one can select a tool material for a given application to assure the chosen performance criterion such as tool life, quality of the machined surface, efficiency, etc. • Proper selection of tool geometry. Because the tool geometry largely defines the state of stress in the deformation zone, stresses, temperatures and relative velocities at the tool–chip and tool–workpiece interfaces, the optimized tribological parameters can be directly used in the selection of proper tool geometry. • Control of machining residual stresses imposed (induced ) in the machined surfaces. The machining residual stresses are determined by the tribological process taking

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• Proper selection of cooling and lubricating media as well as the method of its delivery and application technique. The proper selection and application of a particular medium is only possible when true tribological mechanism of its action is known. The composition and chemistry of cutting fluids can be designed based on the Rebinder effect rather than on other properties (cooling and lubricating as considered today) of a particular cutting fluid.

Uniqueness of this Publication There is a concern that some of the present cutting tool and process designers, manufacturing engineers and engineering students may not be learning enough about metal cutting tribology. Although containing some vitally important information, books to date do not provide methodological information on the subject that can be helpful in making critical decisions in process design, the design and selection of cutting tools, and the implementation of proper machine tool. The most important information is scattered over a great number of research and application papers and articles. Commonly, isolated experimental findings for particular test conditions are reported instead of methodology. As a result, the question: “What would happen if one test parameter is altered?” remains unanswered. Therefore, a broad-based book is needed. The purpose of this book is twofold: First, it aims to summarize the available information on metal cutting tribology with a critical review of work done in the past and thus help specialists and practitioners to separate facts from myths. As shown, the major problem in metal cutting studies is the physically incorrect model used today. Other known problems are just consequences of the implementation of this model. In other words, one fundamental misconception has caused a chain reaction of implementation issues. If a finding or result does not fit the concept of this model then the result is either “silenced,” or bent and twisted to make it fit. Second, it intends to present, explain and exemplify a number of novel concepts and principles in the tribology of metal cutting such as the energy partition in the cutting system, physical efficiency of the cutting system and its practical assessment, versatile metrics of cutting tool wear, optimal cutting temperature and its use in the optimization of the cutting process, the physical concept of cutting tool resource, and embrittlement action of the cutting fluids. The major distinguishing feature of this book is that the practical ways of modeling and optimization of the cutting process are considered using two simple in- and postprocess parameters, namely, the cutting temperature and chip compression ratio that can be measured with sufficient accuracy not only at a research lab but also in the shop floor.

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This makes this book not just another book on the subject, but a practical guide for a wide variety of readers from machining shop practitioners to scientists in the field of metal cutting. For the first time, it attempts to present metal cutting tribology as a science that really works. The book is based on the author’s wide experience in research, practical application and teaching in the area of metal cutting tribology, applied physics, mathematics and mechanics, materials science and engineering systems theory for more than thirty years. Emphasis is placed on the practical application of the results in everyday practice of machining, cutting tool and machining process design. The application of these recommendations will increase the competitive position of the users through machining economy and productivity. It will help them to design better cutting tools and processes, enhance technical expertise and levels of technical services.

Intended Audience The book is intended for four types of readers: (1) metal cutting tool, cutting insert and process designers, (2) manufacturing engineers involved in continuous process improvement via selection of better cutting tools, machines, coolants, optimization of cutting processes and improvement of machining quality, (3) research workers who are active or intend to become active in the field, (4) senior undergraduate and graduate students of manufacturing.

How this Book is Organized The chapters that follow and their contents are listed below:

Chapter 1 Generalized model of chip formation This chapter covers the history, merits and major drawbacks of the single-shear plane model. It is argued that the single-shear plane model is inadequate to explain the real cutting process. It lists and discusses the following principle drawbacks of the single-shear plane model: infinite strain rate; unrealistically high shear strain; unrealistic behavior of the work material; improper accounting of the resistance of the work material to cutting; unrealistic representation of the tool–workpiece contact; inapplicability for cutting brittle work materials; incorrect velocity diagram; incorrect force diagram; inability to explain chip curling. The chapter concludes that any progress in the tribology of metal cutting and in the prediction ability of metal cutting theory cannot be achieved if the single-shear plane model is still at the very core of this theory. Based on the introduced definition of the metal cutting process as a purposeful fracture of the layer being removed, it presents the realistic generalized model of chip formation

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suitable to analyze the tribological processes in metal cutting. The chapter reveals the influence of various factors on the chip structure and thus the tribological conditions. It is argued that the cutting process takes place in the cutting system, so any component of this system and/or any tribological process (taking place in this system) cannot be considered/optimized separately without accounting for the system properties.

Chapter 2 Energy partition in the cutting system This chapter clarifies the energy aspects of metal cutting tribology. It is argued that although many tribological (physical, chemical, etc.) processes can take place at the interfaces in metal cutting, the occurrence of any of these processes is decided by the form and amount of energy available. It considers for the first time the complete model of energy partition and flows in the metal cutting system. The chapter introduces the concept of physical efficiency of the cutting system as the ratio of energies spent on the separation of the layer being removed from the rest of the workpiece and the total energy required by the cutting system to exist. It demonstrates that physical efficiency can be determined knowing the stress–strain curve of the work material, cutting regime and by measuring the cutting force. In a simple and physically grounded manner, the work of plastic deformation done in cutting is correlated with a measurable, post-process characteristic of the cutting process such as the chip compression ratio. The significance of chip compression ratio in the study and optimization of the cutting processes is revealed. Using these results, a practical analysis of the physical efficiency of particular cutting systems is presented and the influence of various parameters and properties on this efficiency is discussed. For a wide range of commonly machined steels, it is demonstrated that the physical efficiency is in the range of 25–60%, so a great margin exists for improving of metal cutting efficiency through optimizing tribological conditions. Two distinctive ways of increasing the physical efficiency of the cutting system are proposed. The first is based on the energy theory of failure and utilizes the interference of the coherent deformation and thermal waves to reduce the required mechanical energy. The second is based on the correlation between the state of stress imposed by the cutting tool in the layer being removed and the fracture strain of the work material.

Chapter 3 Tribology of the tool–chip and tool–workpiece interfaces This chapter argues that because 30–50% of the energy required by the cutting system is spent in useful work, i.e. for the separation of the layer being removed from the workpiece, the rest is spent at the tool–chip and tool–workpiece interfaces. A systemic and systematic approach to the analysis of the tribological conditions at the tool–chip and tool–workpiece interfaces based on the generalized model of chip formation is presented, with the definition and determinations of basic tribological characteristics at these interfaces. The contact stresses, velocities and temperatures are considered. It explains why the similarity method, as compared to numerical methods, is much less sensitive to the particular model used in the thermal analysis of metal cutting.

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The influence of various properties and parameters of the metal cutting process on its tribological characteristics is revealed. The stable and measurable tribological characteristics of metal cutting to be used in the meaningful selection of the parameters and characteristics of the cutting process are identified.

Chapter 4 Cutting tool wear, tool life and physical resource This chapter argues that the existing measures and metrics of tool life and cutting tool evaluation suffer from severe drawbacks. The proper metrics for the assessment of cutting tool wear are presented and evaluated. It offers new effective characteristics of tool wear like the dimension wear rate and the relative surface wear rate. It introduces and explains the concept, physical background and significance of the optimal cutting temperature (the first metal cutting law and its consequences) as the temperature at which the combination of minimum tool wear rate, minimum stabilized cutting force and highest quality of the machined surface is achieved. The validity of the formulated law is illustrated for a vast variety of cutting conditions, work materials and cutting operations. Practical methods for the determination of optimal cutting temperature are offered. The influence of various parameters and characteristics of the cutting process such as the cutting speed, feed, depth of cut, parameters of cutting tool geometry, workpiece material and its diameter on tool life are quantified. Finally, it presents, explains and exemplifies a breakthrough concept of physical resource of the cutting tool in terms of the limiting energy passed through the cutting wedge.

Chapter 5 Design of experiments in metal cutting tests This chapter challenges the existing standards, procedures and policies in metal cutting tests, particularly in the tool-life testing often conducted in tribological studies of the metal cutting process. It explores the methods of design of experiments (DOEs) in metal cutting. Particular attention is paid to the preprocess stage as the most important yet least formalized stage of DOE, where the most crucial decisions affecting the test outcome are made. It explains the basic terminology and requirements to the input and output parameters in DOE particularly to metal cutting. The complete system of metal cutting tests starting from the screening of the DOE is presented, which is implemented at the first stage of testing where the essential parameters are to be identified to the group method of data handling, where the problem of optimization of essential parameters is dealt with. A new sieve DOE is introduced, based upon the Plackett–Burman design ideas, an oversaturated design matrix and the method of random balance. The proposed sieve DOE allows the experimentalist to include at the first phase of the experimental study as many factors as needed and then to sieve out nonessential factors and their interactions by conducting relatively small number of tests.

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It is argued that the Group Method of Data Handling (GMDH), which is applied in a great variety of areas for data mining and knowledge discovery, and, accounting for its basic properties and qualities, seems to be the best option for metal cutting experimental studies as it fully utilizes the system approach. The basic properties and qualities of GMDH are discussed and practical example of its application in tool life testing is presented. A detailed example of the introduced DOEs using deep-hole machining testing is provided.

Chapter 6 Improvement of tribological conditions This chapter classifies the existing methods of improvement into components and the system methods. It focuses on the cutting fluid (coolant) as it accounts for up to 15% of the shop production cost compared to the cutting tool costs, which accounts for up to 7%. The whole process of selection of the proper cutting fluid is discussed. It is argued that the existing methods of cutting fluid tests are inadequate. A new vision of the cutting fluid action is presented, arguing that the cooling and lubricating action are secondary compared to the embrittlement action (the Rebinder effect). It underlines the basic properties of various types of cutting fluids. The basic application aspects of cutting tool coatings are emphasized. It explains that the metallurgical properties of the work material in terms of their influence on the machinability are neglected in research and industry practices, and elaborates on the influence of these properties on tool wear.

Appendix A Basics definitions and cutting tool geometry It presents proper definitions of the parameters of the cutting tool geometry. The most general way of determining the uncut chip thickness as the most important input tribological parameter is provided.

Appendix B Experimental determination of the chip compression ratio (CCR) It describes simple methods of experimental determination of CCR for basic machining operations.

Acknowledgments I wish to thank all my former and present colleagues and students who have contributed to my understanding of metal cutting tribology. A special note of thanks goes to Professors Y.N. Sukhoruckhov, M.O.M. Osman, I.S. Jawahir, J.S. Outeiro, S.P. Radzevich, G.M. Petrosian, A.L. Airikyan and A.Y. Brailov for their valuable help, friendship and continuous support.

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I appreciate the support by my colleagues on the executive board of SME Chapter 69 and on the board of International Journal of Machining and Machinability of Materials (Editor-in-Chief Professor J. Paulo Davim). I wish to express my gratitude to my colleagues and management of Production Service Management Inc. (PSMi) company (COO S. Burk, GM Business Unit Manager T. Markel) for their patient support of my metal cutting and tool application activities in the automotive industry and for utmost efforts to fulfill their responsibilities and to successfully achieve proud results in the quest to be one of the best tool commodity management companies in the world. My special thanks to my wife Dr. Xinran (Sharon) Xiao (R&D, General Motors), for her constructive criticism, tolerance, endless support, encouragement and love.

Viktor P. Astakhov Rochester Hills, Michigan

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NOMENCLATURE

A w = t 1 dw Ac Br (Cpρ)w dcw dw dw1 dw−r D Dw E Ep ex , ey and ez ei erf(z) F FfF FfN Fn Fs Fx , Fy and Fz Fθ f

Cross-sectional area of the uncut chip (m2 ) Cross-sectional area of the chip (m2 ) Briks criterion The volume specific heat of work material (J/(m3◦ C)) Depth of cold working (mm) Cutting width (orthogonal cutting) or the depth of cut (mm) Width of chip (mm) Depth of re-cutting (mm) Similarity criterion that accounts on the parameters of the uncut chip thickness Diameter of the workpiece (diameter of the hole being bored or drilled) (m) Young’s modulus or the modulus of elasticity (MPa) Relative sharpness similarity criterion Direct strains Equivalent strain “Error function” encountered in integrating the normal distribution Friction force at the tool–chip interface (N) Friction force at the tool–workpiece interface (N) Normal force at the tool–chip interface (N) Normal force on the plane which approximates the surface of the maximum combined stress at its final inclination (shear plane) (N) Fs Shear force on the plane which approximates the surface of the maximum combined stress at its final inclination (shear plane) (N) Components of the cutting force in the tool coordinate system (N) Similarity criterion that accounts for the thermal properties of the tool and work materials as well as for the tool geometry Cutting feed (mm/rev)

xx g hr hs hs−opt kw kt kwf Kh lc lc−p lc−e Lw md nw N Nu Pc Pe Po Pr R Re rct rn t1 t2 T TD TUD Tm Ucs Uf ν νf νcf νh νopt νS ν1 ww Wcs α αn α cf βn ε εx , ε y and ε z

Nomenclature Acceleration due to gravity (m/s2 ) Radial tool wear (mm) Relative surface wear rate (µm/103 sm2 ) Optimal relative surface wear (µm/103 sm2 ) Thermal conductivity of work material (J/(m · s· C)) Thermal conductivity of tool material (J/(m · s· C)) Thermal conductivity of the working fluid (J/(m · s· C)) Cooling intensity Contact length (natural) – the length of the tool–chip contact interface (mm) Plastic part of the contact length (mm) Elastic part of the contact length (mm) Length of the workpiece (m) Drill point offset (mm) Workpiece rotational speed (rpm) Normal force at the tool–chip interface (N) Nusselt number Cutting power (W) Peclet criterion (number) Poletica criterion, Po-criterion Prandtl Number Resultant cutting force (N) Reynolds Number Physical resource of the cutting tool (W) Cutting tool nose radius (m) Uncut chip thickness (m) Chip having thickness (m) Tool life (min) Dimension tool life (sm2 ) Specific dimension tool life (103 sm2 /µm) Melting temperature of the work material (◦ C) Total energy entering the cutting system (Ws) Energy to fracture the layer being removed (Ws) Cutting speed (velocity) (m/min) Feed velocity (m/min) Velocity of the cutting fluid (m/min) Dimension wear rate (µm/min) Optimal cutting speed (m/min) Shear velocity (m/min) Velocity of the chip relative to the tool rake face (m/min) Thermal diffusivity of the work material (m2 /s) Power required by the cutting system (W) Tool flank angle (◦ ) Tool normal flank angle (◦ ) Thermal diffusivity of the cutting fluid (m2 /s) Cutting wedge angle in the normal plane (◦ ) Final shear strain True strains along the main axes

Nomenclature εf ε˙ ϕ ϕ1 ϕ2 γ γn γ xy , γ yz and γ zx ηcs κr κr1 λs µ µf νs θr−av θfl−av θfl−max θ ct θ opt ρ ce ρw ρ ct ρcf σ UTS σ YT σc σ c−f σf σi τy τc τ c−f τ in ζ ζt ωac

xxi

Strain at fracture of the work material Strain rate (1/s) Shear angle (◦ ) Approach angle of the gundrill’s outer cutting edge (◦ ) Approach angle of the gundrill’s inner cutting edge (◦ ) Tool rake angle (◦ ) Tool normal rake angle (◦ ) Engineering shear strains Physical efficiency of the cutting system Tool cutting edge angle, major cutting edge (◦ ) Tool cutting edge angle, minor cutting edge (◦ ) Cutting edge inclination angle (◦ ) Mean friction angle at the tool–chip interface (◦ ) Friction coefficient Poisson’s ratio Mean contact temperature at the tool–chip interface (◦ C) Mean contact temperature at the tool–workpiece interface (◦ C) Maximum temperature at the tool flank (◦ C) Cutting temperature (◦ C) Optimal cutting temperature (◦ C) Radius of the cutting edge (m) Density of the work material (kg/m3 ) Density of the tool material (kg/m3 ) Density of the cutting fluid (kg/m3 ) Ultimate tensile strength of the work material (MPa) Yield tensile strength of the work material (MPa) Mean normal stress at the tool–chip interface (MPa) Mean normal stress at the tool–workpiece interface (MPa) Fracture stress (MPa) von-Mises’ stress Yield shear stress of the work material (MPa) Specific frictional force which is the mean shear stress at the tool–chip interface (MPa) Specific frictional force which is the mean shear stress at the tool–workpiece interface (MPa) Strength of adhesion bonds at the tool–workpiece interface (MPa) Chip compression ratio Normalized chip compression ration Angle of action

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CHAPTER 1

Generalized Model of Chip Formation

1.1 Introduction Metal cutting, or simply machining, is one of the oldest processes for shaping the components in the manufacturing industry. It is estimated that 15% of the value of all mechanical components manufactured worldwide is derived from machining operations. However, despite its obvious economic and technical importance, machining remains one of the least understood manufacturing operations due to the low predictive ability of the machining models [1,2]. The old “trial-and-error” experimental method, originally developed in the middle of the nineteenth century (well summarized in [3]) is still in wide use in metal cutting research and development activities. Its modern form, known as the “Unified or Generalized Mechanics Approach,” has been pursued by Armarego and co-workers for years [3], which then spread as the mechanistic approach in metal cutting [4]. It was developed as an alternative to the metal cutting theory because the latter did not prove its ability to solve even the simplest of practical problems. Some researchers even argued about the “advantages of experimental research over theoretical models” [5]. Although a number of books on metal cutting have been published, none of them provides a critical comparison of different theories of metal cutting in their discussion of the corresponding models of chip formation, which constitute the very core of the metal cutting theory. For example, Aramarego and Brown [6] discussed different models of chip formation but did not provide a comparison of their adequacy to reality. After reading these books, practical specialists in metal cutting would not be sufficiently equipped with the knowledge on the advantages and drawbacks of different models, so they may be confused, as to which particular model of chip formation to use in a given practical case. Besides, a great number of articles were published on the subject providing contradictive results and thus adding even more confusion to this matter. When one tries to learn the basics of the metal cutting theory, he/she takes a textbook on metal cutting (manufacturing, tool design, etc.) and reads that the single-shear plane 1

2

Tribology of Metal Cutting

model of chip formation constitutes the very core of this theory. Although a number of models are known to specialists in this field, the single-shear plane model survived all of them and, moreover, is still the only option for studies on metal cutting [7], computer simulation programs including the most advanced Finite Element Analysis (FEA) packages (e.g. [8]) and students’ textbooks (e.g. [9,10]). A simple explanation to this fact is that the model is easy to teach, to learn, and to calculate simple numerical examples on cutting parameter, which can be worked out for students’ assignments [11]. The geometrical relations used in this model seem to be simple and straightforward, and so FEA and simulation packages were developed with rather simple user interfaces and colorful outputs that turned to be attractive for many practitioners in the field. Although it is usually mentioned that the model represents an idealized cutting process [12] and that the shear-angle relationship has been found to be quantitatively inaccurate (p. 48 in [6]), no information about how far this idealization deviates from reality is provided. It is also interesting to note that historically this was the first model to be developed, which was rejected later, and finally widely accepted as “a paramount” today. Even though more realistic models have been developed, for example the model of chip formation with curved shear surface, known as the universal slip-line model developed and verified by Jawahir, Fang and co-workers [13–17], specialists and practitioners in the field still use the significantly inferior single-shear plane model due to its apparent simplicity and transparency. The objective of this chapter is to explain why the single-shear plane model should not be used in metal cutting studies, in general, and in studies of metal cutting tribology, in particular. It also aims to present a new generalized model of chip formation.

1.2 Inadequacy of the Single-Shear Plane Model 1.2.1 Development of the single-shear plane model The single-shear plane model and practically all its “basic mechanics” have been known since the nineteenth century and, therefore, cannot be, even in principle, referred to as the Merchant (sometimes, the Ernst and Merchant) model. This fact was very well expressed by Finnie [18] who pointed out that while the work of Zvorykin and others, leading to the equations to predict the shear angle in cutting, had relatively little influence on subsequent development, a similar work of Merchant, Ernst, and others almost 50 years later has been the basis for most of the present metal cutting analyses. Even the well-known visualization of the single-shear plane model, the so-called card model of the cutting process assigned by many books (e.g. [11]) to Ernst and Merchant, was proposed and discussed by Piispanen years earlier [19,20]. Knowing these facts, one may wonder why Oxley (p. 23 in [21]) stated that “the single shear plane model is based on the experimental observations made by Ernst (1938).” The single-shear plane model of chip formation has been constructed using simple observations of the metal cutting process at the end of the nineteenth century. Time, in 1870 [22] presented the results of his observations of the cutting process. The observations seem to have led to an idealized picture, which is known today as the single-shear plane model for orthogonal cutting, shown schematically in Fig. 1.1(a). The scheme shows the

Generalized Model of Chip Formation

C

3 g

Chip

∆x

t1

t2 g

A

B

Tool

j ∆s

V1

j

V O

Workpiece

(a)

(b) g g

R' m

j Fs Fc FT

N

Fs

F Fc

Fn m−g

FT

R

Fn

F

R m

g N

(c)

(d)

Fig. 1.1. The single-shear plane model of chip formation: (a) as proposed by Time, (b) Card model approximation due to Piispanen, (c) Merchant’s free body diagram for the chip and (d) Merchant’s “convenient” free body diagram.

workpiece moving with the cutting velocity ν and a stationary cutting tool having the rake angle γ. The tool removes a stock of thickness t1 by shearing it (as was suggested by Time) ahead of the tool in a zone which is rather thin compared to its length, and thus it can be represented reasonably well by the shear plane OA. The position of the shear plane is defined by the shear angle φ, as shown in Fig. 1.1(a). After being sheared, the layer being removed becomes the chip having thickness t2 , which slides along the tool rake face. Tresca [23], in 1873, argued that the cutting process is one of compression of the metal ahead of the tool, so chip failure should occur along the path of tool motion. Time in 1877 provided further evidences that the material being cut is deformed by shearing rather than by compression [24]. As shown by Astakhov [25], there are no contradictions between the approaches of Time and Tresca. In the machining of brittle work materials, the fracture of the layer being removed is due to maximum compressive stress; while in the machining of ductile materials these compressive stresses cause plastic deformation by shearing, resulting in ductile fracture of this layer. Zvorykin [26] provided physical explanation for this model as follows: the layer of thickness t1 being removed transforms into a chip of thickness t2 as a result of shear deformation that takes place along a certain unique plane OA inclined to the cutting direction at an angle ϕ. The relationship between the cutting velocity ν and the chip velocity ν1 has also been established in the form as used today [12]. Although the work was recognized and referred for further studies on

4

Tribology of Metal Cutting

metal cutting in Europe, they were somehow completely unknown in North America where theoretical studies on the metal cutting theory began years later [27]. As early as 1896, Briks [28] justly criticized the single-shear plane model pointing out the drawbacks of this model as: the single shear plane and the absence of a smooth connection at point A so that the motion of a particle located in point B into the corresponding location C on the chip is impossible from the point of physics of metal deformation. According to Briks, the existence of a single shear plane is impossible because of two reasons. First, an infinitely high stress gradient must exist in this plane due to instant chip deformation (chip thickness t2 is usually 2–4 times greater than that of the layer to be removed, t1 ). Second, a particle of the layer being removed should be subjected to infinite deceleration on passing the shear plane because its velocity changes instantly from ν into ν1 . Analyzing these drawbacks, Briks assumed that these can be resolved if a certain transition zone, where the deformation and velocity transformation of the work material take place continuously and thus smoothly, exists between the layer being removed and the chip. Briks named this zone as the deformation or plastic zone (these two terms were used interchangeably in his work). Unfortunately, these conclusions were much ahead of his time, and so they were not even noticed by the later researchers until the mid-1950s. Developing the concept of deformation zone, Briks suggested that it consists of a family of shear planes, as shown in Fig.1.2. Such a shape can be readily explained if one recalls the type of tool materials that was available at the time of his study. Neither high-speed steels nor sintered carbides were introduced, thus Briks conducted his experiments using carbon tool steels as the tool material. As a result, the cutting speed was low so that the fanwise shape of the deformation zone shown in Fig. 1.2 was not that unusual as it appears today. To solve the contradictions associated with the single-shear plane model, Briks suggested that the plastic deformation takes place in a certain zone which is defined as consisting of a family of shear planes (OA1 , OA2 , . . ., OAn ) arranged fanwise, as shown in Fig. 1.2. As such, the outer surface of the workpiece and the chip free surface are connected by

Chip

A

n d A1 A 2

A0

d1 j0

Tool

j1

jn

O Workpiece

Fig. 1.2. Briks’ model.

V

Generalized Model of Chip Formation

5

a certain transition line A0 An consisting of a series of curves A1 A2 , A2 A3 , . . ., An−1 An . As a result, the deformation of the layer being removed takes place step-by-step in the deformation zone and each successive shear plane adds some portion to this deformation. The model proposed by Briks solved the most severe contradictions associated with the single-shear plane model. Zorev [29] analyzing the Briks model, did not mention its obvious advantages. Instead, he pointed out the drawbacks of this model: (a) a microvolume of the workpiece material passing the boundary OAn must receive infinitely large acceleration, (b) lines OA1 –OAn cannot be straight but inclined at different angles δ to the transition surface because the boundary condition on the transition surface A1 An requires that these lines form equal angles of π/4 (angle δ1 as shown in Fig. 1.2) with the tangents to this surface in the corresponding points A2 to An . Criticizing Briks model, Zorev did not present any metallographic support to his “π/4” statement even though his book contains a great number of micrographs of partially formed chips. Instead, Zorev attempted to construct a slip-line field in the deformation zone using the basic properties of slip lines. According to his consideration, the deformation process in metal cutting involves shearing and, therefore, is characterized by the lines of maximum shear stress, i.e. by characteristic curves or slip lines (making this “logical” statement assumptions, Zorev automatically accepted that pure shear deformation is the prime deformation mode in chip formation and no strain-hardening of the work material takes place). He considered the deformation zone as a superposition of two independent processes, viz., deformation and friction. Utilizing basic properties of shear lines (term used by Zorev [29]), he attempted to superimpose the slip lines due to plastic deformation and those due to friction at the tool–chip interface. It should be pointed out here that Zorev’s modeling of the deformation zones by slip lines is descriptive and did not follow the common practice of their construction. According to Johnson and Mellor [30], the major feature of the theory of slip lines concerns the manner in which the solutions are arrived at. In any case, such a solution cannot be obtained without constructing the velocity hodograph and verifying boundary conditions before a slip-line field can be drawn. Unfortunately, Zorev did not follow this way although it was already applied to a similar problem by Palmer and Oxley [31]. In Zorev’s opinion, his qualitative analysis was sufficient to “imagine” an arrangement of the shear lines throughout the whole plastic zone “in approximately the form” shown in Fig. 1.3(a). In the author’s opinion, it is next to impossible to figure out the shape of these shear lines knowing only their directions at starting and ending points unless the velocity hodograph is constructed [31,32]. Plastic zone LOM is limited by shear line OL, along which the first plastic deformation in shear occurs; shear line OM along which the last shear deformation occurs; line LM which is the deformed section of the workpiece free surface. The plastic zone LOM includes “a family of shear lines along which growing shear deformation is formed successively” [29]. Zorev stated that such a shape of the deformation (plastic) zone is based on the observations made during multiple experimental studies. Although this model is known in the literature on metal cutting as the Zorev’s model, neither Zorev nor other studies developed a solution for this model, so its significance is of qualitative or descriptive nature. Trying to build a model around the schematic shown in Fig. 1.3(a), Zorev arrived at a conclusion that there are great difficulties in precisely determining the stressed and

6

Tribology of Metal Cutting

M L

t2

M x1

L

O t1

g

P

jsp

j0

j1

K

(a)

N

O

(b)

Fig. 1.3. Zorev’s models: (a) a qualitative model and (b) the final simplified model.

deformed state in the deformation zone he constructed using the theory of plasticity. He pointed out that the reasons for this conclusion were: (a) the boundaries of the deformation zone are not set and thus cannot be defined. In other words, there is no steady-state mode of deformation in metal cutting; the shape of the deformation zone is ever changing, and (b) the stress components in the deformation zone do not change in proportion to one another. As a result of several consecutive steps, Zorev was forced to adopt a significantly simplified model shown in Fig. 1.3(b). This model differs from that shown in Fig. 1.3(a) in that the curves of the first family of shear lines are replaced by straight lines and, in addition, it is assumed that no shearing takes place along the second family of shear lines adjacent to the tool rake face. This model is very similar to that proposed by Briks [28] and Okushima and Hitomi [33]. Moreover, this model levels all Zorev’s considerations made in the discussion of model shown in Fig. 1.2. While studying this simplified model, Zorev further introduced concepts of “specific shear plane” and “specific shear angle ϕsp ” using purely geometrical considerations. According to Zorev, the specific shear plane is the line “passing through the cutting edge and the line of intersection of the outer surface of the layer being removed and the chip.” This specific shear plane is represented by the line OP in Fig. 1.3(b). Zorev admitted that he finally arrived at the model of Time (Fig. 1.1(a)) and using a simple geometrical relationship that exists between two right triangles OKP and ONP, obtained the formula of Time for the chip compression ratio ζ ζ=

cos(ϕsp − γ) sin ϕsp

(1.1)

Assuming further that ϕ1 ≈ ϕsp , Zorev obtained an expression for the final shear strain as ε1 ≈ εsp = cot ϕsp + tan(ϕsp − γ)

(1.2)

Generalized Model of Chip Formation

7


or expressed through the chip compression ratio ζ = t2 t1 and tool rake angle γ, it becomes ε1 ≈ εsp =

1 − 2ζ sin γ + ζ 2 ζ cos γ

(1.3)

Zorev mentioned that because ϕsp < ϕ1 and t1 < x1 , (p. 49 in [29]) Eq. (1.3) gives somewhat “enhanced” values for deformation. Zorev admitted that Eqs. (1.1)–(1.3) were well known in literature sources as derived directly from an examination of the single-shear plane model. However, the way they were derived in Zorev’s book, gives more general solution from which other known models can be obtained. Using purely geometrical considerations, Zorev was able to obtain a generalized solution of the following form: 2ϕsp + µ − γ ≈

π − ψsp , 2

(1.4)

where µ is the mean friction angle at the tool–chip interface. Zorev showed that all the known solutions for the specific shear angle could be obtained from this equation. For the single-shear plane model, the tangent drawn to the workpiece free surface at point P (Fig. 1.3(b)) is a horizontal line and thus ψsp = 0. Substitution of this value into Eq. (1.4) yields 2ϕsp + µ − γ =

π 2

(1.5)

which is the well-known Ernst and Merchant solution [34]. Using the notations ψsp = c1 and (π/2 − γ) = δ, the known Zvorykin solution [26] is obtained ϕsp =

π µ + c1 + δ − 2 2

(1.6)

Using the notations ψsp = c1 and (π/2) − c1 = c, the modified Merchant solution [35] is obtained 2ϕsp + µ − γ = c

(1.7)

If ψsp = µf − γ, the Lee and Shafer solution [36] is obtained ϕ=

π +γ −µ 4

(1.8)

and so on. Analyzing these results, Zorev came to the conclusion that all solutions related to Eq. (1.4) are formal and based on pure geometrical considerations known since the nineteenth century, and thus they have little to do with the physics or even mechanics of metal

8

Tribology of Metal Cutting

cutting because no physical laws (besides the law of simple friction of the chip at the tool–chip interface) and/or principles of mechanics of materials have been utilized in the course of the development of the discussed models.

1.2.2 Merchant’s modifications Card model. According to Merchant, the so-called card model of the cutting process proposed by Piispanen [19] is very useful to illustrate the physical significance of shear strain and to develop the velocity diagram of the cutting process. This model is shown in Fig. 1.1(b). The card-like elements displaced by the cutting tool were assumed to have a finite thickness ∆x. Then each element of thickness ∆x is displaced through a distance ∆s with respect to its neighbor during the formation of the chip. Therefore, shear strain ε can be calculated as ε=

∆s ∆x

(1.9)

and from the geometry of Fig. 1.1(b) it can be found that ε = cot ϕ + tan (ϕ − γ)

(1.10)

Although the card model is used almost in each textbook on metal cutting to explain chip formation, this model has never been considered with the time axis. Such a consideration is shown in Fig. 1.4, where the sequence of formation of two card-like chip elements is illustrated. Let AB be the shear plane and point A the initial point of consideration in frame 1. Due to the action of the penetration force P, the first chip fragment ABCD is

P

P

C B

P

C B

B

A f

D D′ A′

Initial position

1

Time

Initial position

P

F C B

P FC B

DA E 6

A

D A 2

3

P

C B DA

D′

A

G

D E D ′ A′

E′ D′′ A′

5

Initial position

D′

A′

4 Initial position

Fig. 1.4. Card model with the time axis.

Initial position

Generalized Model of Chip Formation

9

formed although it is yet to separate from the workpiece along AD (frame 2). Further tool penetration results in the separation of AD from the workpiece. As such, point A on the chip separated from point A on the workpiece and point D from D (frame 3). Then chip fragment ABCD slides along the shear plane (violating practically all the postulates of the mechanics of continuous media) until the cutting edge reaches point D (frame 4). A new chip fragment D GFE starts to form (frame 5). Then, point D on the chip separates from point D on the workpiece and point E on the chip separates from point E (frame 6). Then the process repeats itself. It should be evident that the separation of the chip fragment from the workpiece is possible if and only if the stress along plane represented in 2D by the lines AD, DE etc. exceeds the strength of the work material and the strain along this plane must exceed the strain at fracture under the given stressed state. In other words, the crack, as a result of separation of the chip fragments along the direction of tool motion, should form in front of the cutting edge as suggested by Reuleaux in 1900 [37], whose work was subject to undue criticism by subsequent researchers. Although Merchant [35] pointed out that thickness ∆x → 0 in the real cutting process, the fracture would take place even for infinitesimal thickness of a chip fragment. Recently, Atkins in his very extensive analysis of the problem [38] pointed out that fracture must occur along the surface separating the layer being removed and the rest of the workpiece. However, what is not pointed out is that if the state of stress ahead of the tool is determined using the single shear plane model then the discussed fracture can never occur in the direction of tool motion. Velocity diagram. When the single-shear plane model was first introduced and discussed, only the tool ν and chip ν1 = νF (νF designation is kept in this section instead of ν1 , as was introduced by Merchant [35]) velocities were considered, as shown in Fig. 1.1(a). Using the above-discussed card model, Merchant developed the velocity diagram shown in Fig. 1.5(a) (similar to that suggested earlier by Zvorykin [26]), which is in almost exclusive use in the modern literature related to metal cutting. Merchant [35] defined νS as the velocity of shear (p. 270 in [35]) and then used this velocity to calculate the work done in shear per unit volume. Shaw transformed this formula to calculate the shear energy (Eq. (3.26) in [12]) as Ws = FAscvvs where Fs is the force acting along the shear plane and Ac (= t1 · dw ) is the uncut chip cross-sectional area. Shaw [12] and Oxley [21] suggested to calculate the rate of strain in metal cutting as ε˙ =

νS , ∆y

(1.11)

where ∆y is the conditional thickness of the shear zone (or plane as per Shaw [12]). Using the velocity diagram developed (Fig. 1.5(a)), Merchant concluded [35] that → → − → ν +− ν 1, νS = −

(1.12)

where νS is the shear velocity. However, if one considers the kinematically equivalent model where the workpiece moves with the cutting velocity while the tool is stationary [11,39] as shown in Fig. 1.5(b),

10

Tribology of Metal Cutting Tool velocity v

t2

g

g

t2

g

g A

A VS t1

VF

VS t1

j V

VF V

B

VS = V + VF

γ

j B

VS = V − VF

g

(a)

(b) VS

VS VF

VF

j V

Workpiece velocity v

j V

(c)

(d)

Fig. 1.5. Velocity diagrams: (a) Merchant’s diagram: the tool moves with the cutting velocity ν and the workpiece is stationary, (b) the tool is stationary and the workpiece moves with the cutting velocity ν, (c) velocity diagram used by Black and (d) velocity diagram by Stephenson and Agapiou.

then Eq. (1.12) is no more valid. Rather it becomes − → → → νS = − ν −− ν1

(1.13)

If it is so, then all the widely used basic metal cutting relationships obtained using Eq. (1.12) are not valid for the case considered. Obviously, the models shown in Figs. 1.5(a) and (b) are kinematically equivalent and so, the magnitude and direction of the shearing velocity MUST be the same. However, this does not follow from the comparison of the velocity diagrams discussed. Some researchers who noticed the problem with the velocity diagram tried to introduce some corrections to this diagram in order to conform to the known vectorial summation as pointed out by Astakhov [40]. For example, Black [41,42] “silently” corrected the velocity diagram shown in Figs. 1.5(a) and (b) offering his version shown in Fig. 1.5(c). Altintas used the same diagram in his book [43]. Although this corrected velocity diagram solves the “sign” problem and this made the derivation of basic kinematic equations correct, the cutting process according to this velocity diagram becomes an energy-generating, rather than an energy-consuming process. This is because the shear velocity, νS and shear force, FS have opposite directions. Trying to resolve the “sign” problem discussed, Stephenson and Agapiou [44] proposed the velocity diagram shown in Fig. 1.5(d), where the direction of chip velocity is assumed to be opposite to the direction

Generalized Model of Chip Formation

11

of its motion. Obviously, this is in direct contradiction with the simple observations of the chip formation process where the chip moves from the chip formation zone. It directly follows from Fig. 1.5(a) that the shear velocity is calculated as νS = cos γ/cos (ϕ − γ)ν and the velocity normal to the shear plane calculated as νn = ν sin ϕ and hence the shear strain that represents chip plastic deformation is calculated as ε=

νS cos γ 1 − 2ζ sin γ + ζ 2 = = νn cos (ϕ − γ) sin ϕ ζ cos γ

(1.14)

Although Eqs. (1.11) and (1.14) are used practically in all the books on metal cutting, there are some obvious problems with these equations in terms of physical meaning and experimental confirmation: • Because νS is high and, according to Fig. 1.5 (a), may well exceed the cutting velocity when the tool rake angle γ is negative (for example, Fig. 9 in [45]), the calculated strain rate in metal cutting was found to be in the range of 104 −106 s−1 or even higher. It is important to realize that this conclusion was made when the experimental technique for measuring material properties and behavior at high strain rates was not yet well developed [25]. Today, when such a technique is common in materials testing and thus the data on the behavior of various materials at high strain rates are widely available [46,47], it can be stated that multiple experimental evidences and test results conducted at low, normal [29] and even ultra-high cutting speeds [48] do not support (both mechanically and metallurgically) the claim about this high strain rate in metal cutting. • If one calculates shear strain using Eq. (1.14) (it can be easily accomplished by measuring the actual chip compression ratio ζ) and then compare the result with the shear strain at fracture obtained in standard materials tests (tensile or compression), one easily finds that the calculated shear strain is much greater (2–5-folds) than that obtained in the standard materials tests. Moreover, when the chip compression ratio ζ = 1, i.e. the uncut chip thickness is equal to the chip thickness so no plastic deformation occurs in metal cutting [49], the shear strain, calculated by Eq. (1.14) remains very significant. For example, when ζ = 1, the rake angle γ = −10◦ , Eq. (1.14) yields ε = 2.38; when ζ = 1, γ = 0◦ then ε = 2; when ζ = 1, γ = +10◦ then ε = 1.68. This severe physical contradiction cannot be resolved with the above-discussed velocity diagram. Multiple known results of the experimental studies on the deformation of the layer being removed using micro-coordinate grid scribed on the side of the workpiece do not support both the velocity diagram discussed and the existence of unique shear plane. These results are well analyzed by Zorev (p. 7 in [29]). Black and Huang [41] and Payton and Black [50] presented the results of the scanning electron microscope (SEM) studies showing that the actual shear velocity as a component of the chip velocity in the deformation zone is rather small (Figs. 10 and 11 in [41] and Fig. 5 in [50]). To understand why the velocity diagram shown in Fig. 1.5(a) is incorrect, one should properly define the meaning of the term “velocity.” It is clear that the velocity is a vector,

12

Tribology of Metal Cutting

so it has magnitude and direction. These two characteristics are not violated in the known velocity diagrams. What is completely ignored in these diagrams is the fact that the velocity as a vector makes sense if and only if it is defined with respect to a reference point or coordinate system. Unfortunately, no literature source defines such a point or a system. Consider the single-shear plane model as shown in Fig. 1.6(a). The stationary xy coordinate system is set as shown in this figure. In this coordinate system, the tool moves with a velocity ν from right to left along the x axis and the workpiece is stationary with respect to the coordinate system introduced. According to Merchant [35], the chip, the workpiece and the tool are rigid bodies having only translation velocities. Therefore, as it is known from kinematics, all points of the chip MUST have the same velocity. Consider a point Mch located on the chip contact side. Point Mch on the chip and point Mt on the tool are coincident points at the moment of consideration. The condition → → of their contact in terms of velocities is: − ν x−Mch = − ν x−Mt . Besides, the velocity of point Mch with respect to the cutting tool is known to be ν1 as shown in Fig. 1.6(a) (wrongly termed as the chip velocity in practically all known literature sources). Therefore, the real

VF

y

Vch

0

x

M ch ′′′′ Mch ′′′ Mch ′′ Mch ′

Mch Mt

V

g V

A′′′ A′′ A′ A

A′′′′

j B ′′′′B′′′ B ′′ B ′ B

(a) y y

g

VS x

x1

ch

V

Pw

j

V

y1

0

x

VF 0 Aw A ch P

A

Vsh Pw ≡ 01

Vn Pch

j

Bw Bch

(b)

g

VF

B

(c)

Fig. 1.6. Analysis of the velocity diagram: (a) successive displacements of point Mch and its velocity components, (b) velocities of coincident points Pch and Pw and (c) the true shear velocity.

Generalized Model of Chip Formation

13

chip velocity in the stationary xy coordinate system can be determined as the vectorial → → → sum of the velocity components mentioned as − ν ch = − ν1 + − ν . As shown in Fig. 1.6(a), as the tool moves, point Mch moves in the direction of the chip velocity νch consequently  , M  , M  , M  , etc. occupying positions Mch ch ch ch Consider two pairs of coincident points located at the ends of the shear plane: points Aw (belongs to the workpiece) and Ach (belongs to the chip); points Bw (belongs to the workpiece) and Bch (belongs to the chip) shown in Fig. 1.6(b). Because these points remain coincident as the tool moves, as shown in Fig. 1.6(a) by points A, A , A , A , A and B, B , B , B , B , respectively, they must have the same velocity along the x axis as required by the continuity conditions [25]. In other words, the low shore of the shear plane also moves with velocity ν. This is also obvious from Fig. 1.6(a) that the shear plane moves with the cutting velocity from left to right as the tool moves. Consider two coincident points: point Pw , which is located on the lower shore of the shear plane and thus belongs to the workpiece, and point Pch , which is located on the upper shore of the shear plane and thus belongs to the chip, as shown in Fig. 1.6(b). Point Pch belongs to the chip and thus its velocity is the same as that of point Mch . Because the lower shore AB of the shear plane moves as a rigid body, point Pw has velocity ν as shown in Fig. 1.6(a). To find the true shear velocity, one should fix one of the two shores of the shear plane. To do this, the moving x1 y1 coordinate system is set as shown in Fig. 1.6(c). The x1 axis of this system is along the shear plane while its y1 axis is perpendicular to the shear plane. The origin 01 coincides with the point Pw so it moves with the velocity ν with respect to the xy coordinate system. It is obvious that since the chip is the only moving component in this new coordinate system, its velocity ν1 has to be considered. The projections of vector ν1 into coordinate axes of the x1 y1 system are shown in Fig. 1.6(c). As shown, they are the normal velocity of the chip, νN and the velocity νsh with which the chip moves along the shear plane, i.e. the true shear velocity, on the assumption that the single-shear model is valid. This conclusion can be supported by experimental observations made by Black and Huang [41] and Payton and Black [50]. Force diagram. Merchant, considering the forces acting in metal cutting, arrived at the force system shown in Fig. 1.1(c) (Fig. 7 in [35]). In this figure, the total force is represented by two equal and opposite forces (action and reaction) R and R , which hold the chip in equilibrium. The force R , which the tool exerts on the chip, is resolved into the tool face-chip friction force F and normal force N. The angle µ between F and N is thus the friction angle. The force R which the workpiece exerts on the chip is resolved along the shear plane into the shear(ing) force, FS which, in Merchant’s opinion, is responsible for the work expended in shearing the metal, and into normal force Fn , which exerts a compressive stress on the shear plane. Force R is also resolved along the direction of tool motion into Fc , termed by Merchant as the cutting force, and into FT , the thrust force. Although this diagram looks logical, there are a number of serious concerns about its physical justification. First, the friction angle µ used in its construction is assumed to be invariable over the entire tool–chip interface. It means that the friction coefficient is constant over the tool–chip interface as assumed by Merchant [35,51] and subsequent researchers. It will be discussed later that if it is so, the distributions of the normal and shear stresses

14

Tribology of Metal Cutting

should be equidistant over this interface. The available theoretical and experimental data [12,29,43,52–56] do not support this assumption. A far more important issue is that Merchant shifted the resultant cutting force R parallel to itself (compare Figs. 1.1(c) and (d)) applying it to the cutting edge “for convenience” (p. 272 [35]). As such, the moment equal to this force times the shift distance was overlooked. Unfortunately, the subsequent researchers who just copied these two pictures did not notice this simple flaw. Moreover, the force diagram shown in Fig. 1.1(d) became known as the classical Merchant force circle and this diagram is discussed today in any book on metal cutting. No wonder that all attempts to apply the fundamental principles of engineering plasticity [57], the principle of minimum energy [58], or define the uniqueness of the chip formation process [57,59] did not yield any meaningful results because the incomplete force system, shown in Fig. 1.1(d) was used as the model. Using Time’s considerations and some of Oxley’s ideas about force arrangement in metal cutting and a possibility of the existence of the additional moment, Astakhov proved theoretically and experimentally that this missed moment is the prime cause for chip formation and thus distinguished the cutting process among other deforming processes [25]. According to the force diagram shown in Fig. 1.1(d), the chip should never separate from the tool rake face because there is no force factor responsible for the chip curling away from this face. Moreover, if the concept of the secondary deformation zone adjacent to the tool rake face is used in the considerations of the single-shear plane model as in practically all known publications on metal cutting [12,21,29,60] starting from Ernst [61], the chip contact layer is subjected to further plastic deformation up to seizure as suggested by Trent [62,63]. As such, the chip formed should curve “inside” the tool rake face because the chip layers adjacent to the chip free surface move freely, i.e. without any further plastic deformation. Unfortunately, these deductions from the single-shear plane model even fail to remotely resemble reality. The chip has a rather limited contact area with the tool rake face and so the chip curling always occurs even in the simplest case of orthogonal cutting presented by Ernst [61] (Fig. 1.7(a)). In the author’s opinion, the prime reason for chip curling follows directly from the stated missed bending moment in the construction of the force diagram shown in Fig. 1.1(d). A simple model, shown in Fig. 1.7(b) clarifies the issue. The resultant force R applied at point B is resolved into two components: normal N and tangential (compressive with respect to the shear plane) F forces. The compressive force, F, forms the uniform (at least, theoretically) compressive stresses σc at the root of the partially formed chipcantilever known as the primary deformation zone, while the normal force imposes the bending moment M = NlB , where the direction of lB is shown in Fig. 1.7(b). This moment causes the compressive stresses (−σ) at the region of the chip free surface and the tensile stresses (+σ) at the chip side that separates from the rest of the workpiece. Therefore, the discussed non-uniform state of stress that causes chip curling as the chip is “born” with the instilled non-uniform stress distribution. Unfortunately, it does not follow from the discussed Merchant force diagram. The missed moment caused a long-standing discussion on the reason for chip curling.

Generalized Model of Chip Formation

15

Chip curves away from the tool rake face

C

lc A lB

j

R

B N

F

O

sc

−s +s (a)

(b)

Fig. 1.7. Chip curling: (a) Ernst’s observation and (b) model showing the action of the bending moment.

A similar result was obtained by Jawahir, Fang and co-workers [13–17] although from a different viewpoint. The similarity, however, is in the recognition of non-uniform chip deformation on its formation as opposed to the uniform shear stress and strain along the straight shear plane according to the single-shear plane model. Resistance of the work material and energy spent in cutting. The foundation of the force and energy calculations in metal cutting is based upon the determination of the shearing force, FS using the equation proposed by Ernst and Merchant in 1941 [34] FS =

τy Ac , sin ϕ

(1.15)

where τy is the shear strength of the work material. According to Ernst and Merchant [34], the work material deforms when the stress on the shear plane reaches the shear strength of the work material. Later researchers published a great number of articles showing that τy should be thought of as the shear flow stress, which is somehow higher than the yield strength of the work material depending on particular cutting conditions [64]. Still, this stress remains today as the only relevant characteristic of the work material characterizing its resistance to cutting [25]. It follows from Fig. 1.1(d), that Fc =

FS cos (µ − γ) cos (ϕ + µ − γ)

(1.16)

16

Tribology of Metal Cutting

and combining Eqs. (1.15) and (1.16), one can obtain Fc =

τy Ac cos (µ − γ) sin ϕ cos (ϕ + µ − γ)

(1.17)

Then the cutting power Pc is calculated as Pc = Fc ν

(1.18)

This power defines the energy required for cutting, cutting temperatures, plastic deformation of the work material, machining residual stress and other parameters. However, everyday practice of machining shows that these considerations do not hold good in reality. For example, machining of medium carbon steel AISI 1045 (tensile strength, ultimate σR = 655 MPa, tensile strength, yield σy0.2 = 375 MPa) results in much lower total cutting force (Fig. 1.8), greater tool life, lower required energy, cutting temperature and machining residual stresses than those obtained in the machining of stainless steel AISI 316L (σR = 517 MPa; σy0.2 = 218 MPa) [65]. The prime reason is that any kind of strength of the work material in terms of its characteristic stresses cannot be considered alone without the corresponding strains, which determine the energy spent in the deformation of the work material [25,49]. Only when one knows the stress and the corresponding strain, one can calculate other parameter outcome of the metal cutting process [49].

P(kN) Total force orthogonal components:

1.20

Pz

Py

Px

Kennametal tool KC850 Feed 0.05 mm/rev Depth of cut 5 mm

1.00 0.80 0.60 0.40 0.20 0 AISI1045 75 m/min

AISI1045 125 m/min

AISI316L 75 m/min

AISI316L 125 m/min

Fig. 1.8. Comparison of the cutting force components (Courtesy Prof. J.C. Oureiro).

Generalized Model of Chip Formation

17

1.2.3 Comparison of the known solutions for the single-shear plane model with experimental results The next logical question is: how good is the single-shear plane model? In other words, how far is this model from reality? Naturally, during the period of 1950–1960, when decent dynamometer and metallographic equipment became widely available, a number of fundamental studies were carried out to answer this question. The results of these extensive researches are well summarized by Pugh [66] and Chisholm [67]. In the author’s opinion, the best research study and a detailed description of the experimental methodology were presented by Pugh [66]. The results obtained by Pugh were discussed by Bailey and Boothroyd ten years later [68]. In his study, all the possible “excuses” for “inadequate” experimental technique were eliminated. The experimental results conclusively proved that for every work material tested, there is a marked disagreement in the “ϕ vs. (µ − γ)” relation between the experiment and the prediction of the Ernest and Merchant, the Merchants, and the Lee and Shafer theories (Eqs. (1.5), (1.7) and (1.8), respectively). The examples of the experimental results obtained are shown in Figs. 1.9–1.12. Figure 1.9 shows the experimental results for lead as the work material. Although such a choice of the work material might seem strange, one should realize that lead definitely has a significant advantage in cutting tests. This is because lead is chemically passive so it does form neither solid-state solutions nor chemical compositions with common cutting tool materials. Therefore, the use of lead as the work material allows to carry out much more “pure” cutting tests. In Fig 1.9, line 1 graphically represents the Ernst and Merchant solution, line 2 represents the Lee and Shafer solution, and line 3 approximates the experimental results. Figure 1.10 shows the results for various tested 40

j + m − g =π/4

2

1 2j + m − g =π/2

3 Shear angle, ϕ(°)

30

20

10

g (°): 60 50 40 30 20 10 0 −10 −20 Dry Lubricated

0 −40

−30

−20

−10

0

10

20

30

40

50

60

m − g (°) Fig. 1.9. Relation between ϕ and (µ − γ) for lead: 1 – Ernst and Merchant solution, 2 – Lee and Shafer solution and 3 – experimental results.

18

Tribology of Metal Cutting 60 50

Shear angle, j(°)

j + m − g =π/4 40

1 2

Tin

2j + m − g =π/2

30 Mild Steel

20 Aluminum

10 Copper

0 −30 −20 −10

0

10

20

Lead

30

40

50

60

m − g (°) Fig. 1.10. Comparison between calculated and experimental results for tin, aluminum, mild steel, lead and copper.

work materials. As seen, the experimental results are not even close to those predicted theoretically. Similar conclusive results were presented by Creveling, Jordon and Thomsen [69] (an example is shown in Fig. 1.11 for steel 1113, where various cutting fluids were used) and by Chisholm [67]. The modified Merchant solution in which the shear to be linearly  stress is assumed  dependent on the normal stress through a factor k1 c = cot −1 k1 τ = τ0 + k1 σ

(1.19)

(according to Merchant, τ 0 and k1 are work material constants) has also been examined for a wide variety of work materials. Equation (1.19) is shown plotted in Figs. 1.12(a) and (b) for copper and mild steel, respectively, together with the experimentally obtained values [66]. As shown, the shear stress does not increase with the normal stress at the rate required by the modified Merchant solution, i.e. to fit the experimental results. In fact, it would appear that the shear stress is almost independent of the normal stress on the single shear plane. The above conclusions were confirmed by Bisacre [66] who conducted similar cutting experiments. The results of these experiments enabled Bisacre to conclude that if the Merchant solution (theory) was correct, there would be a marked effect of the normal stress on the shear stress acting along the shear plane. To support his point, Bisacre noted that the results of tests carried out, in which the same material was subjected simultaneously to torsion and axial compression, showed that the shear strength of the

Generalized Model of Chip Formation 50

19

2j + m − g = π/2

Shear angle, j(°)

40

1 2

30

j + m − g = π/4

20 g (°): 20 25 30 35 40 Air Lusol CCl4

10 0 −20

−10

0

10

20

m − g (°)

30

Fig. 1.11. Relation between ϕ and (µ − γ) for steel SAE 1113.

560

350 Copper

Mild Steel 490

210

Shear stress, t (MPa)

Shear stress, t (MPa)

280

s +k 1 t 0 t47° o t= =C k1

140

g,(°)

Dry Lubricated

20 10

70 0

420

250

t=

k 1s t 0+ 60° t Co k 1=

g,(°)

Dry Lubricated

20 10 0 −20

280

210 0

70

140

210

280

350

0

140

280

420

560

Nornal Stess, s (MPa)

Nornal Stess, s (MPa)

(a)

(b)

700

840

Fig. 1.12. Comparison between the estimated and experimentally obtained relationship “shear stress–normal stress” for copper (a) and steel (b).

material was almost independent of normal stress. As a result, the difference between the theoretical and experimental results cannot be attributed to the effect of the normal stress on the shear strength of the work material, as suggested by Merchant. Zorev also presented clear experimental evidences that the solutions discussed are inadequate [70]. He showed that the Merchant solution is not valid even in the simplest case of cutting at low cutting speeds. Reading this, one may wonder why Zorev did not mention

20

Tribology of Metal Cutting

his findings about the single-shear plane model in his book [29] published five years later. In the author’s opinion, if he had done so, he would have recognized that there was no model of metal cutting available. As a result, he included the above-discussed “general solution” for the single-shear plane model “forgetting” to mention that none of the possible particular solutions to this model is in any reasonable agreement with the experimental results. 1.2.4 Conclusions It is conclusively proven that there is a marked disagreement between the solutions available for the single-shear plane model and the experimental results. Hill, one of the founders of engineering plasticity [71], noticed [72] that “it is notorious that the extent theories of mechanics of machining do not agree well with experiment.” Other prominent researchers in the field conclusively proved that the experimental results are not even close to those predicted theoretically [66,67,69,70]. Recent researchers further clarified this issue presenting more theoretical and experimental evidences [38,73,74]. As one might expect, knowing these results, the single-shear plane model would become history. In reality, however, this is not the case and the single-shear plane model managed to “survive” all these conclusive facts and is still the first choice for practically all the textbooks on metal cutting used today [10–12,42,55,62,75]. In contradiction, all the excellent works showing complete disagreement of this model with reality are practically forgotten and not even mentioned in modern metal cutting books, which still discuss the single-shear plane model as the very core of the metal cutting theory. Moreover, the book “Application of Metal Cutting Theory” [11] is entirely based on this model showing how to apply it in practical calculations although other research works complain about the absence of “predictive theory or analytical system which enables us, without any cutting experiment, to predict cutting performance such as chip formation, cutting force, cutting temperature, tool wear and surface finish” [2]. It should become clear that any progress in the prediction ability of the metal cutting theory could not be achieved if the single-shear plane model is still used. It is necessary to list the major drawbacks of the single-shear plane model: Inherent drawbacks • Infinite strain rate. Infinite deceleration and thus strain rate of a microvolume of the work material passing through the shear plane. • Unrealistically high shear strain. The calculated shear strain in metal cutting is much greater than the strain at fracture achieved in the mechanical testing of materials under various conditions. Moreover, when the chip compression ratio ζ = 1, i.e. the uncut chip thickness is equal to the chip thickness, no plastic deformation occurs in metal cutting [49], the shear strain, calculated by the model remains very significant without any apparent reason for that. • Unrealistic behavior of the work material. Perfectly rigid plastic work material is assumed which is not the case in practice.

Generalized Model of Chip Formation

21

• Improper accounting for the resistance of the work material to cut. The shear strength or the flow shear stress cannot be considered as an adequate characteristic feature with respect to this because, considered alone, the stress does not account for the energy spent in cutting. • Unrealistic representation of the tool–workpiece contact. The cutting edge is perfectly sharp and no contact takes place on the tool flank surface. This is in obvious contradiction to the practice of machining where the flank wear (due to the tool flank–workpiece contact) is a common criterion of tool life [76]. • Inapplicability for cutting brittle work materials. This model is not applicable in the case of cutting of brittle materials, which exhibit no or very little plastic deformation by shear. Nevertheless, the single-shear model is still applied to model the machining of gray cast iron [77], cryogenic water ice [78], etc. Ernst and Merchant-induced drawbacks • Incorrect velocity diagram. In the known considerations of velocities in metal cutting, the common coordinate system is not set, hence the known velocity diagram consists of velocity components from different coordinate systems. As a result, unrealistic velocity components are considered. • Incorrect force diagram. The bending moment due to the parallel shift of the resultant cutting force is missed in the force diagram. As shown [25], this missed moment is the prime cause for chip formation and thus it distinguishes the cutting process among other deforming processes. Moreover, the state of stress imposed by this moment in the chip root causes chip curling. • Constant friction coefficient. Because the friction coefficient at the tool– chip interface can be thought as the ratio of the shear and normal force on this interface, the distributions of the normal and shear stresses should be equidistant over this interface. The available theoretical and experimental data [12,29,43,52–56] do not conform to this assumption.

1.3 What is the Model of Chip Formation? In metal cutting, the term “chip formation” has been used since the ninteenth century. Its initial meaning is the formation of the chip in the primary and secondary deformation zones. Primary attention was devoted to the kinematic relationships, cutting force and contact processes at the tool–chip interface. Later on, the chip-breaking problem became increasingly important with increasing cutting speed and the development of new difficult-to-machine materials. Even though the term “chip formation” is still in use, its original meaning has been transformed. The modern sense of this term implies the chip, which just left the tool–chip interface, is yet to be broken [79,80]. The first widely known classification of the chip was presented by Ernst [61]. According to this classification, there are three basic types of chips found in metal cutting: Type 1 – discontinuous chip (segmental chip) in which initially compressed layer passes

22

Tribology of Metal Cutting

off with each chip segment. According to Ernst, this type of chip is most easily disposed off; finish of the machined surface is good, when pitch of the segments is small; Type 2 – continuous chip with continuously escaping compressed layer adjacent to the tool face. According to Ernst, this chip type is the ideal chip form from the standpoint of quality of finish of the machined surface, temperature of the tool point and power consumption; and Type 3 – continuous chip with built-up edge adjacent to the tool face. According to Ernst, this chip type is commonly encountered in ductile materials. Finish is rough due to fragments of built-up edge escaping with the workpiece [61]. Although these chip types were identified as “classical” [51] and this classification is still widely used today in many books on metal cutting [11,42,81], no one pays attention to either the way these chip types were obtained (cutting regime, tool and work materials, tool geometry, etc.) or to the physical characteristics of these chip types. As is well known [6,12,25,29], the shape of the chip depends primarily on the work material, cutting regime, and tool material and geometry. According to Ernst [61], these chip types were obtained in pure orthogonal cutting at extremely low cutting speed (2 in/min = 0.05 m/min) using very specific work materials (high lead bronze and low carbon, medium nickel chromium steel SAE 3115) and cutting tool (rake angle 23◦ ). From the results of numerous experiments presented by Zorev [29], it is conclusively proven that cutting physics and mechanics of the machining are entirely different at low and at high cutting speeds as well as in the appearance, shape and metallurgy of the chip formed. Using the results of comparison of cutting at low and high cutting speeds obtained by Zorev [29], one can conclude that the classification discussed cannot satisfy growing theoretical and practical requirements to understand the nature of chip formation. As a result, the national industries of the developed countries have adopted more practical classifications of chip type. For example, in Japan, the Subcommittee “Chip Disposal” of the Japan, Society for Precision Engineering (JSPE) adopted a revised system of chip forms, which includes nine chip types, basically classified according to the length of the chip. Standard ISO 3685-1977 gives a comprehensive chip-form classification based on the size and shape of various chips generally produced in metal machining. Other available classifications are discussed in detail by Jawahir and Luttervelt [82]. Unfortunately, the known classifications of the chip formed in machining originate only from the differences in chip appearance, but pay no attention to the physical state of the chip, including its state of stress and strain, hardness, texture, etc. Moreover, neither the complete set of tool geometry parameters nor the cutting regime (for example, the true uncut chip thickness and its width) is taken into consideration [83]. Thus, the known classifications are of a post-process nature rather than being of help in making pre-process intelligent decisions in process optimization and in understanding the tool–chip contact phenomena. A need is felt to develop a model of chip formation that can be used to analyze actual tribological conditions at the tool–chip interface. As such, in addition to the system concept in metal cutting, time dependence of cutting system parameters and their dynamic interactions [25,83] and the time axis will be added to this model.

Generalized Model of Chip Formation

23

1.4 System Concept in Metal Cutting The system concept in metal cutting was first introduced by Astakhov and Shvets [83]. According to this concept, metal cutting is considered to be taking place in a system consisting of the following components: the tool, the workpiece and the chip. The process of metal cutting is defined as a deforming process, which takes place in the components of the cutting that system are so arranged through which the external energy applied causes the purposeful fracture of the layer being removed. This fracture occurs due to the combined stress including the continuously changing bending stress causing a cyclic nature of this process. The most important property in metal cutting studies is the system time. The system time was introduced as a new variable in the analysis of the metal cutting system and it was conclusively proven that the relevant properties of the cutting system’s components are time dependent [83]. The dynamic interactions of these components take place in the cutting process causing a cyclic nature of this process.

1.5 Generalized Model of Chip Formation Although the basics of the cutting tool geometry are discussed in Appendix A, it is necessary to set here proper definitions for the terms “cutting edge” and “cutting wedge” that will be used in further considerations because these two are mostly misunderstood and thus misused in the literature on metal cutting. One should clearly realize that the cutting edge is the line of intersection of the face and the flank surfaces. Therefore, the basic characteristics of the cutting edge should be thought of as those that can be attributed to a line. When one talks about cutting edge geometry, it should be understood only as the geometric characteristics of a line in terms of its length, 3D shape, etc. It is highly improper to speak about cutting edge wear because a line cannot have any wear. The cutting tool geometry can be discussed as attributed to the point of the cutting edge considered. In this case, however, this line should be considered as belonging to the corresponding rake or flank surface so that the geometry of the corresponding surface should be meant. The working part of the cutting tool is referred to as the cutting wedge, which is enclosed between the tool rake and flank contact surfaces intersecting to form the cutting edge. This cutting wedge is under the action of stresses applied on the tool–chip and tool–workpiece contact surfaces. Moreover, due to the heat that flows into the cutting tool, this wedge has high temperature. Therefore, when it is said that the cutting tool penetrates into the workpiece, the penetration of the cutting wedge is meant because the configuration of the cutting tool outside the cutting wedge does not affect the metal cutting mechanics and physics of the cutting process (at least theoretically when the tool is considered to be infinitely rigid as in any model of chip formation). Consider the cutting wedge (tool) starting to advance into the workpiece under the action of the applied penetration force P, as shown in Fig. 1.13(a). As a result, the stresses grow in the workpiece and, as might be expected, the maximum stress occurs in front of the

24

Tribology of Metal Cutting

Workpiece

Cutting tool

P

P

(a)

(b)

P

(c)

Fig. 1.13. Cutting tool starting to advance into the workpiece.

cutting edge due to stress singularity at the point. When this maximum reaches a certain limit, depending on the properties of the work material the following happens: • If the work material is brittle, a crack appears in front of the cutting edge (Fig. 1.13(b)). Later on, this crack leads to the final fracture of the layer being removed. • If the work material is ductile, a visible crack would not be readily observed because of the “healing” effect of plastic deformation. Instead, a certain elastoplastic zone forms in the workpiece in front of the tool rake face, as shown in Fig. 1.13(c). The dimensions of the plastic and elastic parts of this zone depend on ductility of the work material. It is understood that for a perfectly plastic work material, the elastic zone would not form at all, while for a perfectly brittle material the plastic zone would never form. This simple qualitative consideration illustrates that the properties of the work material play an extremely important role from the beginning of chip formation. Because the general behavior of work materials in metal cutting can be classified as ductile or brittle depending upon the degree of plastic deformation that a material exhibits in its deformation, this fact should be organically incorporated in the chip formation model. As such, a certain criterion (or criteria) should be established to classify a given material as brittle or ductile because no perfectly brittle or perfectly ductile work materials exist in reality. In mechanical metallurgy, elongation or strain at fracture is usually used for such a purpose [81]. It would be necessary to emphasize here, however, that none of the known criteria of ductility (brittleness) can be regarded as a mechanical property of the work material because the same material may exhibit considerably different elongations and strain at fracture depending upon the loading conditions which include the state of stress, strain rate, temperature, etc. Unfortunately, today the decision about ductility of the work material is routinely made on the basis of its mechanical properties obtained in one of the standard material tests under uniaxial stress state, room temperature and moderated strain rate (4–5 orders lower than that found in metal cutting).

Generalized Model of Chip Formation

25

P P

(a)

(b)

(c)

Fig. 1.14. Difference in deformation pattern in compression and in cutting: (a) specimen with the scribed grid, (b) distortion of the initial grid in compression and (c) distortion of the initial grid in cutting.

Another important issue follows from Fig. 1.14. Figure 1.14(a) shows a specimen made of a ductile material with the grid scribed on its cylindrical surface. Figure 1.14(b) shows grid distortion occurred in compression where simple shearing is the prime deformation mode. Figure 1.14(c) shows grid distortion occurred in cutting. If one compares deformation patterns due to compression and cutting, one observes significant difference because simple shearing is not the prime deformation mode in metal cutting, as suggested by the single-shear plane model discussed earlier. This simple fact is known from mechanics of materials and could be easily confirmed by anyone conducting a simple test similar to that shown in Fig. 1.14. Unfortunately, the known works on metal cutting do not account for this simple result.

1.5.1 Brittle work materials Consider the machining of a brittle work material using the system approach in metal cutting. Two basically different cases are possible here depending on the arrangement of the components of the cutting system. The first one takes place when the components of the cutting system are arranged so that the resultant force R acting on the chip from the tool rake face intersects the conditional axis of the partially formed chip, as illustrated in Fig. 1.15. As such, the bending moment that rose in the root of the chip (Section 1.1) due to the action of this force, causes chip fracture along the path where the combined stress (compression and bending) exits the fracture stress for this work material. Figure 1.16 illustrates a system consideration of the model shown in Fig. 1.15. Phase 1 illustrates the initial stage when the tool comes in contact with the workpiece.

26

Tribology of Metal Cutting Conditional axis of the chip R 1

1

Fig. 1.15. Resultant force R intersects the conditional axis of the partially formed chip (after Astakhov [18]).

P

4

P

3

P

2

P

1

System Time

P

8

P

7

P

6

P

5

System Time

Fig. 1.16. System consideration of the model shown in Fig. 1.15.

To advance the tool into the workpiece, the penetration force P has to be applied to the tool, provided the workpiece is fixed rigidly. The interaction between the tool and the workpiece results in the formation of a stressed zone ahead of the tool (Phase 2). Because there are absolutely no brittle work materials, this zone consists of the elastic and plastic parts although its plastic part is small compared to the elastic part. When the maximum stress in the stressed zone reaches a certain limit, a crack forms in front of the cutting edge (Phase 3). Further increase in the penetration force P leads to the development of this crack formed (Phase 4). At this stage, cutting completely resembles splitting. Due to

Generalized Model of Chip Formation

27

small plastic deformation allowed by the ductility of even very brittle materials, the formed crack opens and the partially formed chip comes into contact with the tool rake face (Phase 5). Since then, the partially formed chip serves as a cantilever beam loaded by the compressive force and the bending moment, as shown in Fig. 1.15. As a result, combined stress acts at the chip root which serves as the chip-cantilever support. When this combined stress reaches a certain limit, fracture of the chip-cantilever takes place at its root (support) (Phase 6). As such, the separate, almost rectangular chip elements are produced (Phase 7) as observed in the cutting of brittle work materials using cutting tools with positive rake angles [84,29]. This chip is common in the automotive industry in the machining of slip yokes made of ductile cast iron. This chip type may be referred to as the regularly broken chip. The second case in the machining of brittle work materials takes place when the components of the cutting system are so arranged that the resultant force R does not intersect the conditional axis of the partially formed chip, as shown in Fig. 1.17(a). As such, no bending moment can arise due to the interaction of the tool rake face and the partially formed chip. As a result, there is no bending stress in the root of the chip-cantilever so that the final fracture of this chip (and thus the layer is removed) takes place only due to the compressive stress imposed by the penetration force P. The chip formed consists of irregularly shaped fragments of the work material and dust which are the same as in the fracture of the work material under compression (Fig. 1.17(b)). This dust is the well-known nuisance of machine shops dealing with machining of cast irons. Figure 1.18 presents a system consideration of the model shown in Fig. 1.17(a). Phase 1 illustrates the initial stage when the tool is forced by the penetration force P into the workpiece. As a result, the compression stress grows in the workpiece starting from the first contact point. Further advance of the cutting tool leads to the development of crack network pre-rupture evolution (Phase 2), which eventually leads to the compression-type fracture of the layer being removed (Phase 3). Further advance of the cutting tool (Phase 4)

Conditional axis of the partially formed chip P

R

P

(a)

(b)

Fig. 1.17. Resultant force R does not intersect the conditional axis of the partially formed chip (a) that results in common fracture of a brittle material under compression (b) (after Astakhov [18]).

28

Tribology of Metal Cutting

P

4

P

P

3

2

P

1

System Time

P

8

P

7

P

6

P

5

System Time

Fig. 1.18. System consideration of the model shown in Fig. 1.17(a).

leads to the bulk rupture of the layer being removed and the formation of the chip in the form of irregularly shaped pieces of the work material and dust (Phases 5 and 6). Then a new cycle of chip formation begins (Phase 7) which repeats itself in two stages (Phase 8 is the same as Phase 4). The chip produced in this process can be referred to as the irregularly broken chip. The two cases discussed in the machining of brittle materials can be related to work materials of low ductility (elongation is ≤2%). Many real work materials used in everyday practice are not so brittle. For example, malleable cast irons exhibit elongation from 1 to 10%, spheroid graphite cast irons – from 3 to 15%, ductile cast iron – minimum. 10%, lead bronzes – from 5 to 15%, etc. Therefore, these materials exhibit appreciable plastic deformation before fracture. Figure 1.19 shows system consideration of the model of chip formation for such materials. As shown, the surface of the maximum combined stress (compressive and bending stresses) is located at a certain angle to the direction of tool penetration. Although the fracture of chip fragments takes place along this surface, this fracture is not purely brittle because the layer being removed deforms plastically prior to this fracture. The chip formed in this process can be referred to as the deformed fragmentary chip. This model can be considered as a transitional model between the discussed model of chip formation in the machining of brittle materials and that of ductile materials discussed further although it should possibly be attributed to the machining of brittle materials. This is because the crack originates at the tool cutting edge (as it is clearly shown in Fig. 1.19) and then runs to the workpiece free surface. However, it is necessary to mention that transition in the mechanics and physics of chip formation from brittle to ductile zone is itself continuous by nature while any model is discrete. Therefore, one should clearly

Generalized Model of Chip Formation

29

(a)

(b)

(c)

(d)

Fig. 1.19. Quick-stop micrographs of partially formed chip. Workpiece material: lead bronze; orthogonal cutting on a shaper; cutting conditions: cutting speed 35 m/min, uncut chip thickness 2.2 mm, dry cutting; cutting tool material: P10; Tool geometry: rake angle – 15◦ , flank angle – 8◦ (after Astakhov [18]).

realize that no single model could satisfy the properties of work materials used today. In fact, a set of models should be developed consisting of a number of different models each suitable in some range of properties of the work and tool materials and cutting conditions. As new work and tool materials are introduced, this set should be updated with new models accounting for new mechanics and the physical process with respect to the cutting process.

1.5.2 Ductile work materials When considering ductile work materials, different distinctive models are developed depending on the properties of the work material, contact conditions at the tool–chip interface and tool geometry [25]. The basic case of chip formation in cutting ductile materials takes place when no seizure occurs at the tool–chip interface and this is the most common case in the cutting of most engineering materials. At the initial stage of chip formation, an elastoplastic zone forms in front of the cutting edge due to the stress concentration, which is due to the pure compression of the layer to be removed.

30

Tribology of Metal Cutting Chip

Tool

S 1

P

P Q

1 L

(a)

(b) S S 1

P Q

1 L

(c)

(d)

Fig. 1.20. The interaction between the tool rake face and the partially formed chip: (a) partially formed chip-cantilever subjected to the penetration force P from the tool rake face, (b) two components of the penetration force P, (c) maximum plastic deformation in the bending occurs in the vicinity of the cantilever’s free surface and (d) deformation takes place along the line of maximum combined stress 1-1.

As a result, the plastic deformation of this layer takes place by pure shearing during this stage. As the tool advances further, the plastically deformed part of the layer being removed gradually comes into close contact with the tool rake face. When full contact is achieved, this part serves as a cantilever and subjected to the penetration force P from the tool rake face, as shown in Fig. 1.20(a). This penetration force can be resolved into two components namely, compressive force Q, acting along the direction of the conditional axis of the partially formed chip, and bending force S, acting along the transverse direction, as shown in Fig. 1.20(b). Therefore, the partially formed chip can be considered as a cantilever beam subjected to the mutual action of the compressive force Q and bending moment M (= SL). When it happens, the state of stress in the chip root (the cantilever support) becomes complex because it includes a combination of the bending and compressive stresses. As such, the slip-line field in the deformation of such a cantilever can be thought of as the superposition of the slip-line field due to bending and that due to compression.

Generalized Model of Chip Formation

31

The known studies of slip-line deformation fields of cantilevers with curved contours [30,85] show that the maximum plastic deformation in the bending occurs in the vicinity of the cantilever’s free surface adjacent to its clamped side. Figure 1.20(c) shows the intensity of this deformation by the corresponding slip lines. As it is well known [30,85], the plastic deformation under compression is the result of successive shear deformation taking place along the direction of the maximum shear stress. As such, this direction is oriented at the angle of 45–90◦ depending on the ductility of the material. When these two slip-line fields are superimposed, the deformation process of the partially formed chip shifts from pure shearing to complex shearing. As such, the surface of the maximum combined stress becomes curved (as shown by its trace 1–1) and the maximum deformation occurs at both the ends of this surface, as shown in Fig. 1.20(d). The discussed state of stress can be easily verified by a simple FEA and by observation of grain structure of a partially formed chip [25] and by the experimental results obtained by Zorev [29]. Figure 1.21 presents a system consideration of the model shown in Fig. 1.20(d). Phase 1 shows the initial stage. When the tool is in contact with the workpiece, the application of the penetration force P leads to the formation of deformation zone ahead of the cutting edge. The workpiece first deforms elastically and then plastically. As a result, a certain elastoplastic zone forms ahead of the tool that allows the tool to advance further into the workpiece so that a part of the layer being removed comes in close contact with the tool rake face (Phase 2). When full contact is achieved, the state of stress ahead of the tool becomes complex including a combination of the bending and compressive stresses. The dimensions of the deformation zone and the maximum stress increase with penetration force P. When the combined stress in this zone reaches the limit (for a given work material), a sliding surface forms in the direction of the maximum combined stress (Phase 3). This instant may be considered as the beginning of chip formation.

P

P

3

2

P

1

System Time

P

6

P

5

P

4

System Time

Fig. 1.21. System consideration of the model shown in Fig. 1.20(d).

32

Tribology of Metal Cutting

As soon as the sliding surface forms, all the chip-cantilever material starts to slide along this surface and thus along the rake face (Phase 4). Upon sliding, the resistance to tool penetration decreases, leading to a decrease in the dimensions of the plastic part of the deformation zone. However, the structure of the work material, which has been deformed plastically and now returns to the elastic state, is different from that of the original material. Its appearance corresponds to the structure of the cold-worked material. Experimental studies [25,29,86–88] showed that the hardness of this material is much higher than that of the original material. The results of the experimental study using a computer-triggered, quick-stop device proved that this material spreads over the tool–chip interface by the moving chip that constitutes the well known chip contact layer (Phase 5), which is now believed to be formed due to the severe friction conditions in the so-called secondary deformation zone [29]. The sliding of the chip fragment continues until the force acting on this fragment from the tool reduces, because a new portion of the work material is entering into contact with the tool rake face. This new portion attracts a part of the penetration force P. As a result, the stress along the sliding surface diminishes, becoming less than the limiting stress that ceases the sliding. A new fragment of the chip starts to form (Phase 6). The chip formed in this way is referred to as the continuous fragmentary chip. It has a sawtoothed free side and a non-uniform strength along its length. The shear strength of the fragments is much greater than that of fragment connections. Therefore, obstruction-type chip breaker works well to break this chip type into manageable-size pieces convenient for proper chip disposal. Comparison of the predicted and actual chip structures shows that they are identical (Fig. 1.22). Increasing the cutting speed leads to significant reduction in the “average pitch” between two successive “teeth” on the chip free surface and to further distinction between the chip fragments and their connectors. Such a chip is known as the shear localized chip.

Fig. 1.22. Structure of the continuous fragmentary chip: (a) prediction and (b) experiment.

Generalized Model of Chip Formation

33

It is worthwhile to notice an essential fact that stems from the considerations of this model. The chip formation process is cyclic so that the resistance to the tool penetration into the workpiece varies within each cycle of chip formation and is thus time dependent. Therefore, it should be expected that the bending moment and thus the bending stress in the deformation zone should vary over this cycle. Naturally, the cycles in chip formation are not exactly the same due to the variations in the crystalline structure of the work material (dislocation density varies over the volume of the workpiece), presence of inclusions, residual stresses from the previous manufacturing operations and many other factors. What does not change is the sequence “loading-fracture” found in any cycle. This cyclic nature of the chip formation process determines the inherent dynamic nature of the metal cutting process. Depending upon the variations in the magnitude of the penetration and other forces, which are components of the resultant cutting force, the performance of the machining system (which includes the cutting system, fixture, machine, etc.) is affected in different ways. Naturally, the response of the components of the machining system would depend on the static and dynamic stiffness and rigidity of the whole machining system. Due to great variety of work materials, cutting tools, machining regimes, configurations of the workpiece and many other factors, the magnitude and its variation (including frequency), point of application, and direction of the resultant cutting force vary within a very broad range. In the author’s opinion, misunderstanding of the above-described interactions of the components of the machining system led to the interpretation of the cutting force as having a stochastic nature (for example [89–91]). If it would be so, the whole cutting process should be considered as stochastic and thus its prediction cannot be made on the basis of its theoretical analysis.

1.5.3 Highly ductile work materials Bearing in mind the presence and significance of the bending stresses in the deformation zone [25], we are now ready to consider the known difficulties in the cutting of highly ductile materials. It is well known that increasing the ductility of the work material lowers its machinability. By this, it is meant that both the cutting temperature and power per unit volume of metal removed will increase [92]. This conclusion, however, stems from the practice of metal cutting rather than from the known theories of chip formation. As discussed above, the known model recognizes simple shearing as the only cause for chip formation and thus cannot explain why machining of a work material with lower shear strength requires more energy than that with a much higher shear strength. To understand the phenomenon, a special experiment was carried out [87]. Two specimens – the first made of AISI steel 1045 (yield strength σYT = 525 MPa, ultimate strength σUTS = 585 MPa, elongation at break δ = 10%), the second made of much more ductile steel AISI 302 (σYT = 250 MPa, σUTS = 610 MPa, δ = 67%) were machined using the same cutting regime (cutting speed was 90 m/min; feed – 0.12 mm/rev; depth of cut – 1.5 mm; no cutting fluid, a P10 carbide cutter with rake angle of −8◦ ). In the experiment, the chip compression ratio, ζ was measured and the deformed structure of the chip produced was analyzed. For the first specimen, it was found that ζ1 = 1.87, while for the second ζ2 = 5.22. As shown in Chapter 2, the degree of plastic deformation and thus the energy required by the cutting system in the machining of steel AISI 302 is much greater than that in the machining of AISI steel 1045.

34

Tribology of Metal Cutting Tool

Workpiece

Tool

Workpiece

y1

y1

y

y x

x

x1

x1

(a)

(b)

(c) Fig. 1.23. Chip formation in the machining of a ductile material: (a) chip compression ratio ξ = 2, (b) chip compression ratio ξ = 5 and (c) typical chip structure in the cutting of a highly ductile material (×200).

Moreover, it was also found in this test that the temperature of the chip is almost 200% higher in the machining of steel AISI 302. While the reason for higher plastic deformation in the machining of highly ductile work materials will be analyzed later, the changes in the chip deformed structure with increasing ductility of the work material can be explained as follows. Figure 1.23(a) shows the model of chip formation in the machining of a ductile material where the chip compression ratio ξ = 2, while Fig. 1.23(b) shows the model of chip formation in the machining of a highly ductile material where the chip compression ratio ξ = 5. In both the models, the right-hand coordinate system is set as follows: The x axis coincides with the direction of the sliding plane (approximation of the surface of the maximum combined stress) in the current chip formation cycle. The y axis is perpendicular to x axis, as shown in Figs. 1.23(a) and (b). The z axis (not shown) is perpendicular to the x and y axes. Because it was found experimentally that in metal cutting the change in the volume in the chip plastic deformation is negligibly small [12,25,29], the following expression for

Generalized Model of Chip Formation

35

strains is valid εx + εy + εz = 0,

(1.20)

where εx , εy and εz are the true strains along the corresponding coordinates. Referring to Figs. 1.23(a) and (b), consider a volume of the work material located between the two successive sliding planes (shown as hatched area in Figs. 1.23(a) and (b)). The plastic deformation of this volume can be represented by corresponding strains as εx = ln

x1 , x0

εy = ln

y1 , y0

εz = ln

z1 , z0

(1.21)

where, x0 , y0 , z0 and x1 , y1 , z1 are the dimensions of the discussed volume along the corresponding coordinates before and after deformation, respectively. It is known [25] that, when properly measured, the chip width is practically equal to the width of cut, which yields z0 = z1 , thus εz = 0. Accounting for this result, substituting Eq. (1.20) into Eq. (1.21) and ignoring signs, one can obtain ln

y1 x1 = ln =0 x0 y0

or

x1 y1 = x0 y0

(1.22)

A very important conclusion immediately follows from Eq. (1.22): increasing chip thickness x1 (i.e. the chip compression ratio ζ) leads to the directly proportional reduction of distance y1 between the two successive sliding planes, increasing the number of sliding planes per unit length of the chip. To support this conclusion, Fig. 1.23(c) shows a micrograph of the chip structure formed in the cutting of the second specimen. In this micrograph, a great number of traces of the sliding planes, one closely followed by another, can be observed that makes its appearance quite similar to the continuous chip (Section 1.5.5). However, the conditions of chip formation considered show that this chip is still a continuous fragmentary chip with a very small distance between two successive fragments. Naturally, the breakability of this kind of the chip deteriorates with increasing ductility of the work material. A similar picture can be observed in the micrograph of the quick-stop section through copper chip presented by Trent and Write (Fig. 4.27 in [62]). As the number of sliding planes per unit length of the chip increases, heat generation due to the relative sliding of chip fragments increases proportionally. This explains the much higher temperatures in the machining of highly ductile materials. Quite often, the chip formed has a cherry-red color due to its high temperature. It is necessary to mention, however, that transition in the mechanics and physics of chip formation from ductile to highly ductile zone is itself continuous by nature while any model is discrete. At a certain point, when ductility of the work material becomes great enough to develop high temperatures at the tool–chip interface, periodic and then permanent seizure can occur.

36

Tribology of Metal Cutting

1.5.4 Model of chip formation when periodic seizure occurs at the tool–chip interface Seizure as a phenomenon in metal cutting was probably first introduced and described by Zorev [29], although Zorev did not study this phenomenon thoroughly. The reason for that is simple: not many work materials having the properties which lead to seizure as well as the corresponding machining regimes, were used in the 1960s. Trent has presented the evidence for seizure in his articles and books for more than 20 years and his results are summarized in his book [93]. However, in his article [63] Trent complained that though appreciation of the condition of seizure at the tool–chip interface is fundamental to the understanding of the whole process of metal cutting, it has not been recognized by most engineers or by tribologists. In the excellent Wear – A Celebration Volume (1984), the hypothesis of seizure in metal cutting was dismissed in two paragraphs by J.M. Challen and P.L.B. Oxley as a phenomenon which “is not ruled out for certain conditions.” This is a strange reason because many phenomena in metal cutting occur only under certain conditions. In the author’s opinion, the concept of seizure is not accepted by other researchers simply because the tribology of seizure is not discussed thoroughly and thus understood. For example, Trent and Write associated seizure with the built-up edge (p. 41 in [62]) and thus its influence on chip formation and tool wear at relatively high cutting speeds, although it is a well-established fact [29] that no built-up edge can occur at this speed range. In other words, it is not sufficient to point out the existence of a phenomenon and present purely experimental evidences of its occurrence. Rather, the physical conditions of its occurrence and its influence on the process outcomes should be clearly established. Unfortunately, this is not the case with seizure and thus available books on metal cutting do not mention this term [11,43,44,55]. This situation may be explained by the fact that Trent was concerned mainly with the metallographic aspect of the problem and did not correlate it with the other important mechanical and physical phenomena occurring at the tool–chip interface during the chip formation of different work materials. In his book [93], Trent first presented the singleshear plane model of chip formation and then discussed the evidence of seizure which has little correlation with this model. It appears that the lack of the model of chip formation under conditions of seizure causes the situation discussed. Therefore, it was found necessary to clarify the place of seizure in chip formation. Seizure, having adhesion nature, ceases a normal chip sliding over the tool face because of the continuous contact in both the hills and valleys of the tool–chip contact surface. For seizure to occur, a high contact temperature is the prime condition. As explained above, in the cutting of highly ductile work materials the energy consumption per unit volume of the removed material is high, and when it is combined with the low thermoconductivity of the work material, high temperatures develop at the tool–chip interface which might lead to seizure. Figure 1.24 presents a model of chip formation when seizure occurs at the tool–chip interface [83,87]. In this model, it is assumed that the temperature and contact pressure at the tool–chip interface have reached a level when seizure occurs so that the force required for the sliding of the chip over the tool rake face (the tool–chip interface ab) becomes greater than that required for the plastic deformation of the layer being removed ahead of the partially formed chip. Surface ac separates the motionless chip and the

Generalized Model of Chip Formation

37

g1 P

b

c

y1 d e

a R1

Fig. 1.24. Model of chip formation when seizure occurs at the tool–chip interface (after Astakhov [78]).

deformation zone and surface ad separates this zone from the undeformed layer being removed (the boundary of plastic and elastic zones in the work material). Boundaries ac and ad are located by the angle ψ1 relative to each other. As the tool progresses in the cut, the material in the wedge-shaped zone acd are compressed, deformed and thus squeezed in the direction of free boundary cd. When the load from the cutting tool increases further, deformed plastic zone acd in front of the tool expands. As a result, the angle ψ1 increases. This increase can take place only due to the rotation of the boundary ad in the clockwise direction, as the plastic deformation cannot progress in the direction of boundary ac because the formed chip is already severely deformed compared to the rest of the work material. Finally, rotating boundary ad takes its limiting position ae, and the final configuration of deformed plastic zone ace is formed. As such, gradually increasing the angle γ1 up to 90◦ , leads to a change in the mode of deformation from the compression-type to the shear-type. When γ1 = 90◦ , fracture and thus sliding of the partially formed chip takes place along the boundary ae. At the instant preceding this fracture, the resistance to the tool penetration is at its maximum and the direction of the reaction R1 (from the elastically deformed part of layer being removed) becomes parallel to the tool rake face while the normal pressure at the tool–chip interface becomes insignificant. As a result, force R1 shears the chip and deposit ace along the tool rake face. The region in the vicinity of the cutting edge becomes clear and the sliding of the chip over the tool rake face resumes until a new cycle of seizure and deposit formation occurs. Figure 1.25(a) presents system considerations of the model shown in Fig. 1.24. In this figure, Phase 1 shows the instant when the sliding plane forms in the direction of the maximum combined stress. When the chip slides over the tool rake face, the contact length is heated up mainly due to chip deformation and friction. As the contact temperature at the tool–chip interface grows, adhesion between the tool rake face and the chip along the tool–chip interface increases as the materials of the chip fills even the smallest roughness on the contact surface. In effect, the adhesion force at the tool–chip interface increases. When the contact temperature reaches a certain level (for given work

38

Tribology of Metal Cutting

1

(c)

2

(a)

c a

g1

3

d R1 4

(d)

P qr−av P

(b)

qr−av

Time Fig. 1.25. System consideration of chip formation under conditions of seizure: (a) phases in chip formation, (b) corresponding variations of the cutting force and temperature, (c) micrograph of the continuous fragmentary humpbacked chip (×50) and (d) the continuous fragmentary humpbacked chip formed when no stage of free sliding occurs at the tool–chip interface (×50).

and tool materials), the force required for chip sliding becomes greater than that of the plastic deformation of a part of the layer being removed ahead of the tool. As such, the chip and the tool are interlocked to such an extent that “normal” sliding cannot occur. The interlocked part of the tool–chip contact changes the “normal” chip formation process causing an increase in the resistance to tool penetration. As a result, the cutting force increases leading to an increase in the dimensions of the plastic zone in front of the tool (Phase 2). In turn, the increase in size of the plastic zone leads to the formation of a growing deposit on the interlocked part (Phase 3). Here, zone acd is the current plastic zone formed after the chip sliding over the tool face ceases due to seizure. Its boundary ac separates the plastic zone and the motionless chip while its boundary ad separates this zone from the undeformed layer being removed. As the tool progresses in the cut, the material in the plastic zone acd is compressed and squeezed in the direction of its only free surface cd so that zone acd expands. As the chip is motionless and has already been severely deformed, the plastic zone expands into the workpiece. During this

Generalized Model of Chip Formation

39

transformation, the angle γ1 gradually increases up to 90◦ that, in turn, leads to a change in the deformation mode of the grooving deposit from the compression-type to the sheartype. When γ1 approaches 90◦ , reaction force R1 (from the elastically deformed part of layer being removed) changes its direction to become parallel to the tool rake face (Fig. 1.25(a), Phase 3). When the penetration force P reaches a certain limit, reaction force R1 becomes great enough to shear the whole deposit along the tool–chip interface. Once the deposit has been sheared off, the “normal” chip formation takes place until the contact temperature becomes high enough to start the formation of a new deposit. To verify the model discussed experimentally, a cutting experiment was carried out. A low carbon, low alloy steel (0.12% C, 1% Cr, 1% Mn, 1% Ti) was machined at a cutting speed of 70 m/min, feed of 0.14 mm/rev, depth of cut of 2.0 mm with a M30 tool having the rake angle of −8◦ . The penetration force P and the temperature at the tool–chip interface were measured. Variations in the tool–chip contact temperature θr−av and in the penetration force P were recorded simultaneously. Figure 1.25(b) presents a sample of the results obtained. As shown, the penetration force increases during the period of time of deposit formation while the contact temperature decreases because there is no relative tool–chip sliding within this period. The chip formed according to the model described is referred to as the continuous fragmentary humpbacked chip and its basic appearance is shown in Fig. 1.25(c), where the zones of normal sliding and those of deposit formation can be clearly observed. This chip cannot be regarded as continuous because its structure includes chip fragments and their connectors although the distance between successive connectors is very small. Figure 1.25(d) shows an extreme case of this type of the chip where no stage of free sliding occurs at the tool–chip interface. The structure of this chip consists of series of deposits following one another. As described, this chip formation process has a periodic or almost periodic nature. As a result, the thickness of the chip formed almost shows periodic variations when the chip formation conditions repeat themselves. Experience shows that the appearance of the continuous fragmentary humpbacked chip may vary significantly, although the mechanism of its formation is still the same. An emergency situation can occur in this type of cutting when the adhesion forces at the tool–chip interface are so high that the chip–tool contact cannot be separated by the growing cutting force. As a result, the chip cannot slide over the tool face and the chip formation process becomes impossible. Moreover, when the growing cutting force reaches a certain limit, tool breakage is unavoidable. As such, the weakest components of the tool will be deformed and/or fractured.

1.5.5 Model of chip formation for cutting with a high positive rake angle Figure 1.26(a) shows a model of chip formation for cutting a ductile work material with the cutting tool having a high rake angle. As such, the rake angle may reach 30–45◦. The reduction in the amount of plastic deformation with increasing rake angle eventually leads to the condition where the angle θγ between the plane of maximum shear-stress and the direction of the compressive force P, approaches 90◦ . Such a representation allows one to compare the compression of the work material by the tool face with the pressing

40

Tribology of Metal Cutting

g qg D

L 0

0.4

0.2

0.7

P

0.2

(a)

1 2

C

sxy (GPa) M

(b)

Fig. 1.26. (a) A model for cutting with a high rake angle and (b) the chip structure obtained in this process (after Astakhov [78]).

of a wedge-shaped workpiece between a pair of flat plates inclined with a small angle relative to each other. In cutting, the tool rake face plays the role of one of the plates, while the layer being removed where the plastic deformation has not yet occurred (the conditional boundary between the plastic and elastic zone is shown in Fig. 1.26(a) as line ML) plays the role of another plate. Under such conditions, the main part of the work material flows in the direction of the “thick” part of the wedge-shaped plastic deformation zone CMLD; the internal layers flow much more intensively than the external layers; and the deformation rate in the “thin” part of deformation zone CMLD is much higher than that in the “thick” part. To support this statement, the stress distribution in this zone is shown by isolines obtained using a FEM simulation. Foregoing considerations of cutting with high rake angles lead to the conclusion that if the interaction of metal cutting system components is as shown in Fig. 1.26(a), the work material fractures only along the line separating the workpiece and the layer being removed so there are no other sliding planes formed in the chip. As a result, a special chip type referred to as the continuous uniform-strength chip with wedge-shaped texture is formed. To verify this model, a number of cutting tests have been carried out. Figure 1.26(b) shows a micrograph of the structure of the chip obtained in a turning cutting test conducted under the following conditions: cutting speed ν = 120 m/min, depth of cut d = 2 mm, feed f = 0.15 mm/rev, work material AISI steel 1015 with the initial hardness 150 HV, rake angle γn = 40◦ , tool material P20, and no coolant was used. The wedge-shaped fragments in the chip texture can be clearly seen in the micrograph

Generalized Model of Chip Formation

41

(Fig. 1.26(b)) where a higher strain is observed at the “thin” part of grains. To verify this, a microhardness scanning test was carried out. It was found that the average microhardness of the “thick” parts is 188 HV while that of the “thin” parts is 320 HV which is in full agreement with the results of FEM analysis shown in Fig. 1.26(a) by isobars of shear stress component σxy (GPa). 1.5.6 Generalization The above-discussed models allow us to propose a generalized model for chip formation shown in Fig. 1.27. The model includes three basic regions, A, B and C, which correspond to the properties of the work material. Region A in this model generalizes models and chip structures obtained in the machining of brittle materials. An analysis of these models shows that while cutting the brittle

Work Material

Chip Structure

Model of Chip Formation

Separate almost rectangular chip fragments the regularly broken chip

Brittle

A

Irregularly shaped fragments of work material and dust the irregularly broken chip

Regularly shaped separate fragments with some plastic deformation deformed fragmentary chip Continuous fragmentary chip with easy-to-distinguish elements and connectors

Ductile

B

Continuous chip having practically uniform strength along its length Continuous fragmentary chip with difficult-to-distinguish elements and connectors

Highly Ductile

C

Unstable chip having variable thickness along its length the continuous fragmentary humpbacked chip

Fig. 1.27. Generalized model of chip formation.

42

Tribology of Metal Cutting

work materials, the chip shape is still a controllable parameter. When compression and bending act together, much less energy has to be supplied to the machining zone and better working conditions (at least the absence of dust) may be achieved. The tool geometry plays an important role here. If selected properly, the chip formed has the appearance of separate, almost rectangular elements and, therefore, is referred to as the regularly broken chip. As one might argue, however, a positive rake angle is not very practical in cutting cast irons and similar brittle work materials due to the possible presence of significant amount of hard inclusions. In such a case, a normal grade of tungsten carbide, as a tool material, cannot withstand peak bending loads. As a result, practically all recommendations for the tool geometry are the same suggesting a high negative rake angle that unavoidably leads to the second model in Region A (Fig. 1.27). The chip formed consists of irregularshaped fragments of work material and dust, therefore, is referred to as the irregularly broken chip. To overcome this barrier and to shift from the irregularly broken to the regularly broken chip type, one should use positive rake angle when feasible. Modern submicrograin carbides possess sufficient fracture toughness to withstand the discussed inclusions successfully. The same logic is now applicable to high-speed machining of high-silicon aluminum alloys widely used in the automotive industry. For many years, polycrystalline diamond (PSD) brazed and indexable cutting inserts were used for this purpose with negative rake angles. With the recent development of ultramicrograin PCDs and advanced tool materials, cutting tool companies (for example, Kyocera, SP3, Mapal) began to offer PCD insert with high positive (up to 10◦ ) rake angles that significantly improve machining (tool life, machined surface integrity, reduce the cutting force, etc.) of such alloys. Unfortunately, the recommendations for suitable tool geometries do not reflect the great advances made in the last 5–10 years in the properties of tool materials and coatings. The last model in Region A is a kind of transitional model applicable to technically brittle materials. As discussed above, some plastic deformation of the layer being removed is allowed before a fragment of this layer separates from the workpiece. Region B of the model shown in Fig. 1.27 covers two basic chip structures found in the machining of most engineering materials. The chip formed according to the first model in this region is referred to as the continuous fragmentary chip. As discussed, it is characterized by non-uniform strength along its length. The chip fragments and their connectors can be clearly distinguished on a micrograph of the chip structure. The difference in the appearance of the chip fragments and connectors increases significantly with the cutting speed. The chip formed according to the second model in this region is referred to as the continuous chip. The major characteristics of its structure and properties were discussed above. Additionally, it is necessary to point out that this chip is characterized by the maximum (compared to the other chip structures) ratio “chip hardness/hardness of the original work material” and by excessive length of the tool–chip interface. Region C of the model shown in Fig. 1.27 represents two basic cases in the cutting of highly ductile work materials. The first model in this region is basically the same as the first model of Region B. However, great toughness of highly ductile materials results in greater chip deformation and, as discussed above, the distance between the two successive fragments becomes much smaller than that in the cutting of ductile materials.

Generalized Model of Chip Formation

43

The chip formed is referred to as the continuous fragmentary chip with difficult-todistinguish elements and their connectors. The second model of Region C of Fig. 1.27 represents unstable chip formation. The instability occurs mainly due to the periodic seizure at the tool–chip interface. The chip formed under these conditions is referred to as the continuous fragmentary humpback chip. This type of chip is common in the machining of aerospace materials such as chromium- and/or high nickel-based alloys. The models of chip formation presented in the generalized model shown in Fig. 1.27 can be referred to as basic. The appearance of the chip may vary significantly depending on the tool geometry, machining regime, contact conditions at the tool–chip interface and other factors involved in chip formation. 1.6 Influence of Cutting Speed So far, the models of chip formation process are considered irrespective of the cutting speed, which actually has a marked influence on this process. The cutting speed affects the chip formation process in two major ways. First, it changes the strain rate in the deformation zone and thus affects the resistance of the work material and the thermal energy generated in its deformation. Second, it affects the tool–chip relative speed and the natural length of the tool–chip interface and thus affects the tribological conditions at this interface. These two aspects are discussed in detail in Chapter 3. As a result, the chip characteristics like the structure, appearance and physico-mechanical properties heavily depend on the cutting speed. Ekinoviˆc and coauthors [94] carried out a number of milling tests and studied the influence of cutting speed on the chip structure and appearance for different work materials shown in Table 1.1. The test results are shown in Figs. 1.28(a)–(d). Figure 1.28(a) shows the influence of cutting speed for work material 1 (low-carbon steel). When this material is machined at a cutting speed of ν = 150 m/min, the classical continuous fragmentary chip is produced (micrograph 1 in Figs. 1.28(a) and 1.29(a)). Its average microhardness is much higher than that of the original work material that reflects high plastic deformation of this chip. This conclusion is also fully supported by relatively high (for this kind of work material) chip compression ratio, which is

Table 1.1. Work materials used in the test [94]. Chemical composition (%)

Metallurgical state C Work material 1 – annealed Work material 2 – austenized Work material 3 – annealed Work material 4 – tempered

Si

Mn

P

S

Cu

0.17 0.27 0.41 0.019 0.013 0.31

Cr

Ni

Mo

0.12 0.08 0.01

V

Al

–

0.053

0.04 0.45 1.55 0.028 0.035 0.53 18.26 8.80 0.63 0.08 0.017

0.62 1.00 0.59 0.017 0.004 0.26

5.46 0.23 1.21 0.46 0.028

44

Tribology of Metal Cutting

300

296 HV

Microhardness, HV

266 HV

1

200

Chip compression ratio x = 3.4 156 2 100

Initial microhardness of the work material

x = 1.3

150

Cutting speed, v ( m/min)

1500

(a) Work material 1 500

Microhardness, HV

420 HV

400

266 HV

300

3

221 200

100

4

Initial microhardness of the work material

150

Cutting speed, v ( m/min)

1500

(b) Work material 2

Microhardness, HV

500

470 HV

457 HV

400 5

300 282 200

100

Initial microhardness of the work material

6 fseg = 33.2 kHz High-Speed Region

Conventional Speed Region

150

Cutting speed, v ( m/min)

1500

(c) Work material 3 Fig. 1.28. Relations between the morphology of the chip and the cutting speed for different work materials (Courtesy of Prof. S. Ekinoviˆc).

Generalized Model of Chip Formation

45

800

Microhardness, HV

756 HV

700

742 HV

660 HV

9 fseg = 15.6 kHz

8 fseg = 3.84 kHz

629

720 HV

600 500 10 fseg = 100.6 kHz

7

400

50

150

300

1500

(d) Work material 4 Fig. 1.28.—Continued.

100 µm

(a)

100 µm

(b)

Fig. 1.29. Structures of the chip produced during machining of work material 1 at (a) ν = 150 m/min and (b) ν = 1500 m/min (Courtesy of Prof. S. Ekinoviˆc).

calculated as the ratio of the chip thickness (0.34 mm) and the uncut chip thickness (0.10 mm), i.e. ξ = 0.34/0.10 = 3.4. Increasing the cutting speed to ν = 1500 m/min does not change the type of chip structure produced (micrograph 2 in Figs. 1.28(b) and 1.29(b)). The reduction of chip plastic deformation occurred during the chip formation results in smaller chip compression ratio (ξ = 1.3) and in lowering the average chip microhardness. Figure 1.28(b) shows the transformation of the chip structure with the cutting speed for work material 2 (austenized stainless steel). The structure of the chip produced during machining with ν = 150 m/min (micrograph 3 in Figs. 1.28(b) and 1.30(a)) also belongs to the classical continuous fragmentary chip with saw-toothed (also referred to as serrated

46

Tribology of Metal Cutting

Crack

20 µm

100 µm

(a)

100 µm

(b) Fig. 1.30. Structures of the chip produced during machining of work material 2 at (a) ν = 150 m/min and (b) ν = 1500 m/min (Courtesy of Prof. S. Ekinoviˆc).

and fragmented) free surface. The cracks formed in the formation of this chip cannot be completely “healed” by plastic deformation, so their tips can be clearly observed at higher magnification (Fig. 1.30(a)). High average microhardness of this chip is a consequence of high plastic deformation during its formation. Increasing the cutting speed to ν = 1500 m/min does not change the type of chip structure produced, but extensive heat generation in the formation of this chip causes its very high temperature than annealing the deformed structure of this chip (micrograph 4 in Figs. 1.28(b) and 1.29(b)) and thus lowers its final microhardness. However, a SEM image of the free side of this chip (Fig. 1.30(b)) reveals the presence of the fragments. Figure 1.28(c) shows the transformation of the chip structure with the cutting speed for work material 3 (high-carbon steel, annealed). The structure of the chip produced during machining with cutting speed ν = 150 m/min (micrograph 5 in Figs. 1.28(c) and 1.30(a)) also belongs to the classical continuous fragmentary chip similar to that shown in Fig. 1.29(a). However, high carbon content in this steel lowers its allowable plastic deformation to fracture and thus the chip compression ratio for this chip is ξ = 1.7. Increasing the cutting speed to ν = 1500 m/min changes the chip structure and thus its

Generalized Model of Chip Formation

47

100 µm

(a)

100 µm

(b)

(b)

Fig. 1.31. Structures of the chip produced during machining of work material 3 at (a) ν = 150 m/min and (b) ν = 1500 m/min (Courtesy of Prof. S. Ekinoviˆc).

appearance. As clearly seen in micrograph 6 in Figs. 1.28(c) and 1.31(b), the structure of the chip obtained is similar to the continuous fragmentary humpback chip. A SEM image of the free side of this chip (Fig. 1.31(c)) reveals the presence of the fragments and their connectors. Figure 1.28(d) shows the transformation of the chip structure with the cutting speed for work material 4 (high-carbon steel, tempered). The structure of the chip produced during machining with a cutting speed of ν = 50 m/min (micrograph 7 in Fig. 1.28(d)) belongs to the classical continuous fragmentary chip similar to that shown in Fig. 1.28(a). Increasing the cutting speed to ν = 150 m/min (micrograph 8) leads to the onset of unstable chip formation with low frequency fcf = 3.84 kHz (the concept of frequency of chip formation is explained later in this chapter). Relatively low temperature causes the formation of almost separate chip fragments having relatively low strength of their connectors. Further increasing the cutting speed to ν = 300 m/min does not change the structure of the chip while resulting in higher chip formation frequency fcf = 15.6 kHz (micrograph 9 in Fig. 1.28(d)). As such, the strength of the chip connectors increases. Even further increase in the cutting speed to ν = 1500 m/min does not change the

48

Tribology of Metal Cutting

structure of the chip while resulting in higher chip formation frequency fcf = 100.6 kHz (micrograph 10 in Fig. 1.28(d)). Similar influence of the cutting speed on the chip structure and chip compression ratio was revealed in the experiments conducted by Tónshoff et al. [95]. In their experiments, much greater cutting speeds (up to 4000 m/min), different tool and work materials were used. Comparison of their results with those presented in Fig. 1.28 reveals that the frequency of chip formation (segmentation) depends both on the cutting speed and work material. It is pointed out in both the studies that when chip distinctive segmentation is the case (i.e. unstable chip formation takes place according to our current consideration), the hardness of the border of a chip segment is severely deformed compared to the center of this fragment.

1.7 Formation of Saw-Toothed Chip Normally, when the work material is very ductile, there is always a great spread between its ultimate tensile, σUTS and yield tensile, σYT strengths. For example, AISI steel 303 has the following characteristics: σUTS = 620 MPa and σYT = 320 MPa while cold drawn AISI steel 1045 has σUTS = 625 MPa and σYT = 530 MPa. Moreover, some ductile materials are characterized by a great dependence of their strength on temperature. When such a material is machined, the saw-toothed chip is normally produced. This type of chip is a particular case of the continuous fragmentary chip, where the size of “tooth” becomes noticeable. Talantov [96] was probably the first to prove that thermodynamic equilibrium in the deformation zone governs the chip formation process for the temperature-sensitive ductile work materials. He suggested that the position of the shear plane changes during a chip formation cycle in order to maintain this equilibrium during plastic deformation of the chip on its formation. He also noticed that the grain structure of the chip varies over a chip formation cycle. Figure 1.32 illustrates a cycle of chip formation of chip fragment B of the saw-toothed continuous fragmentary chip. There are four distinctive phases in this cycle: • Phase 1 is the initial stage of the cycle considered, where chip fragment A just finished its formation. The surface of the maximum combined stress, approximated by straight line ab, is located at an angle ϕmax with respect to the direction of the cutting speed. • Phase 2 is the beginning of the formation of fragment B. Due to the combined action of the compressive and bending stresses and due to plastic deformation, the inclination of the surface of maximum combined stress decreases. As such, this surface is located at a certain intermediate angle ϕint1 . The temperature of the chip formation zone increases as a direct result of plastic deformation. • Phase 3 concludes the first stage of plastic deformation of fragment B. During this first stage (Phases 1–3) fragment B is subjected to severe plastic deformation due to great spread between the ultimate tensile, σUTS and yield tensile, σYT strengths of

Generalized Model of Chip Formation

A a

j min

P

P

A B

j int1

b

P a b

B

2

1

System Time

tch A B

j max

b

3

pch

A

a

B

49

A P

P a B

a

j max

j int2

b

b 4

5 System Time

Fig. 1.32. System consideration of the model of chip formation of the saw-toothed continuous fragmentary chip.

the work material. The amount of plastic deformation gained at the end of Phase 3 is maximized so the resistance of the work material is the greatest due to its maximum strain hardening. As a result, the inclination of the surface of maximum combined stress is minimum which is thus characterized by the angle ϕmin . As a result of severe plastic deformation of partially formed chip fragment B, the temperature in the deformation zone increases to its maximum at this stage. This temperature lowers the resistance of the work material. • Phase 4 shows an intermediate stage of the second stage of the formation of chip fragment B where the surface is located at a certain intermediate angle ϕint2 . The amount of plastic deformation gained by this chip fragment decreases as this angle increases. This phase eventually leads to Phase 5 (which is the same as Phase 1), where the chip fragment B just finished its formation. The surface of the maximum combined stress, approximated by straight line ab, is again located at angle ϕmax with respect to the direction of the cutting speed. The temperature due to plastic deformation is at a minimum at this stage. Then a new cycle begins. The pitch of the chip, pch and the depth of the chip profile, tch depend on the properties of the work material (spread between its ultimate and yield tensile strengths under a given state of stress in the deformation zone; dependence of its strength on temperature; toughness, which defines the energy spent in its plastic deformation), on the machining regime (the pitch depends on the cutting speed while the profile depth depends on the cutting feed (uncut chip thickness)) and on the tool geometry (the normal rake and inclination angles), which define the state of stress in the deformation zone.

50

Tribology of Metal Cutting

Figure 1.33 shows the results of FEM modeling for the case considered. The following conditions were considered in this modeling: • Tool: normal rake angle γn = 0◦ , normal flank angle αn = 7◦ , inclination angle λS = 0◦ , radius of the cutting edge ρce = 0.005 mm, tool material is K15. • Work material: AISI steel 316L, σUTS = 517 MPa and σYT = 218 MPa. • Cutting regime: cutting speed ν = 75 m/min, uncut chip thickness t1 = 0.2 mm, width of cut dw = 2 mm. Figures 1.33(a) and (b) show the state of the deformation zone for Phases 3 and 5, respectively. As shown, these results correspond to the model shown in Fig. 1.32. Figures 1.33(c) and (d) show the temperature distribution in the deformation zone for these two stages. These results correspond to the model description showing the above-described temperature variation in the deformation zone. Figures 1.33(e) and (f) present the stress distribution in the deformation zone for the phases discussed. Therefore, these FEM results fully support the described physical model of saw-toothed chip formation. To verify the discussed model experimentally, a series of cutting tests were carried out. The following work materials were used in the tests: (a) AISI steel 1045 HR ASTM A576 RD, and (b) AISI stainless steel 303 ANN CF RD ASTM A582 93. The composition, element limits and deoxidation practice were chosen to comply with the requirements of standard ANSI/ASME B94.55M-1985. To simulate the true orthogonal cutting conditions, the special specimens were used [25]. After being machined to the configuration, the specimens were tempered at 180–200◦ C to remove the residual stresses. The hardness of each specimen has been determined over the whole working part. Cutting tests were conducted only on the specimens where the hardness was within the limits of ± 10%. Special parameters of the microstructure of these specimens such as the grain size, inclusions count, etc. was determined for the initial workpiece structures (shown in Figs. 1.34(a) and 1.35(a)) using quantitative metallography. The samples of the chip, obtained in cutting experiments, are shown in Figs. 1.34(b) and 1.35(b). The chip structure shown in Fig. 1.34(b) is a typical structure of continuous fragmentary chip obtained in the machining of ductile materials, the strength of which has low sensitivity to temperature. Very fine, irregular and heavy deformed (the microhardness of the chip is almost two times higher (285 HV) than that of the original material (163 HV)) “teeth” are formed on the chip free surface when this kind of steels are not pre-hardened or modified to low or high alloys. A similar structure is shown in Fig. 1.28 for work material 1. As shown from this figure, a significant increase in the cutting speed leads to coarsening of the “teeth” on the chip free surface due to high temperature involved in the chip formation. The chip structure shown in Fig. 1.35(b) is a typical saw-toothed continuous fragmentary chip. To support the explanations given to the model shown in Fig. 1.32, the variation of plastic deformation during a chip formation cycle should be clearly shown. As such, higher plastic deformation should be the case during the loading stage of a cycle (Phases 2 and 3 in Fig. 1.32) and lower plastic deformation during the unloading stage of this

Generalized Model of Chip Formation

51

(a)

X 400

(b)

X 200

Fig. 1.34. Work material – AISI 1045 steel. Micrographs of (a) the initial structure and (b) the chip structure obtained in orthogonal cutting test with a cutting speed of 60 m/min, equivalent cutting feed of 0.2 mm/rev. Etched with 10 ml Nital and 90 ml alcohol (after Astakhov [18]).

cycle (Phases 4 and 5 in Fig. 1.32). Figure 1.36 shows a fragment of the saw-toothed chip shown in Fig. 1.35(b). As clearly shown, the deformed structure of this fragment consists of two distinctive zones: zone of high plastic deformation where the grains are severely deformed and zone of low plastic deformation where the grains are moderately deformed. The visual observations discussed may be subjective. To overcome these difficulties, two-dimensional microhardness maps of the chips were taken to map out different zones through the chip section. As discussed in [25], microhardness is uniquely related to

52

Tribology of Metal Cutting

(a)

X 400

(b)

X 150

Fig. 1.35. Work material – AISI 303 stainless steel. Micrographs of (a) the initial structure and (b) the chip structure obtained in orthogonal cutting test with cutting speed of 60 m/min, equivalent cutting feed of 0.2 mm/rev. Etched with 40 ml hydrofluoric (HF), 20 ml nitric acid and 40 ml glycerine (After Astakhov [18]).

the plastic strain of a deformed body as well as to the shear stress gained at the last stage of deformation. In this study, a Leco M400-G2 microhardness tester was used. This machine operates by automatically indenting the specimen over an area defined by a grid of measurement points. At each location, indentation depth and load are measured as the load is applied. Microhardness was determined using the principles outlined in ISO standard for Instrumented Hardness Tests, ISO DIS 14577. The position of the surface is identified by fitting a polynomial to the initial 5% of the loading curve.

Generalized Model of Chip Formation

53

Zone of low plastic deformation Zone of high plastic deformation

X600 Conditional boundary between two zones

Fig. 1.36. A chip fragment of the chip shown in Fig. 1.36(b).

The displacement at maximum load incorporates elastic and plastic deformation. A linear fit to the top 20% of the unloading curve (representing elastic unloading) is extrapolated to zero load to determine the depth of the material in contact with the indenter at maximum load. The test results show that for the chip fragment shown in Fig. 1.36, average microhardness in the zone of high plastic deformation is 335 HV while that in the zone of low plastic deformation is 225 HV. These results conclusively prove the adequacy of the model of saw-toothed chip formation shown in Fig. 1.32. 1.8 Frequency of Chip Formation As the chip formation process appears to be cyclic, its frequency is of interest. The frequency of chip formation can be measured by calculating the number of teeth produced in unit time as proposed by Talantov [96]. However, there are two drawbacks in this method. First, the pitch of the saw-tooth chip (pch in Fig. 1.32) is not always easy to measure because a lengthy mounting process is required. The accuracy of the evaluation is not high because the pitch may vary (for example, due to the variation in the microstructure of the work material) over the length of the chip and thus a rather long chip should be taken into evaluation, which may not be feasible. If only a short chip fragment (for example as shown in Fig. 1.37) were considered, the averaging of pch would not guarantee correct results. Second, it is not applicable for the analysis of the

54

Tribology of Metal Cutting

X100

Fig. 1.37. Quick-stop micrograph of a partially formed chip. Work material is AISI steel 4140. Cutting conditions: cutting speed ν = 85 m/min, feed f = 0.14 mm/rev, rake angle γn = 12◦ , flank angle αn = 10◦ . Orthogonal dry cutting.

continuous fragmentary chip when the depth of profile tch (Fig. 1.32) is very small as, for example, the chip shown in Fig. 1.34. Lindberg and Lindstrom [97] proposed direct measurement of this frequency using a digital spectrum analyzer. One common method of visualizing a dynamometer signal is in the time domain (Fig. 1.38(a)). This representation often plots the signal value (commonly a voltage or current that represents the measurement of force, temperature or strain) as a function of time. Another useful signal representation is the frequency-domain view of the signal (Fig. 1.38(b)). This representation is typically based on a variation of

(a)

(b)

Fig. 1.38. Cutting force signal in the time domain (a) and its representation in the frequency domain (b) obtained using LabView FFT by National Instruments Co.

Generalized Model of Chip Formation

55

the Fourier Transform and commonly plots the frequency or phase content of a signal as a function of frequency. By examining the frequency-domain view of the signal, useful information about the measured signal can be derived that might not be immediately apparent from an examination of the time-domain representation. For a given signal, the power spectrum gives a plot of the portion of a signal’s power (energy per unit time) falling within given frequency bins. The most common way of generating a power spectrum is by using a discrete Fourier transform [98]. It can be accomplished using a digital spectrum analyzer [25,97]. Figures 1.39(a)–(c) show the examples of the results of a study of the chip formation frequency of different work materials (the test methodology is discussed in detail in [99]). These figures show the frequency power spectra of cutting force obtained in the machining of different materials at the same cutting regimes and dimensions of the workpieces. As shown, the dynamic response of the machining system, including machine tool, depends not only on the system’s geometry and cutting regime used, but also on a particular workpiece material used. The results of this study reveal that the frequency of the chip formation process primarily depends on the cutting speed and on the work material. The cutting feed and the depth of cut (>1 mm) have very small influence on this frequency. The dependence of the chip formation frequency on the cutting speed was obtained by taking power spectra similar to those shown in Figs. 1.39(a)–(c) at different cutting speeds. The results are shown in Fig. 1.40. The results obtained also show that when the dynamic experiments are conducted properly, i.e. when the noise (for example, due to the misalignment of the workpiece and other machining system inaccuracies) is eliminated from the system response, the amplitudes of peak at the frequency of chip formation are the largest in the corresponding autospectra. Unfortunately, this fact is not considered in the dynamic analysis of the machining systems where the cutting process as the main source of vibration is practically ignored.

1.9 Formation of the Segmental Saw-Toothed Chip The formation of the segmental saw-toothed chip similar to that shown in Fig. 1.28(d) (micrographs 8–10) attracted the attention of some researchers due to wider use of highspeed machining and a great number of difficult-to-machine alloys. Shaw [45] claims that he was the first to publish a micrograph of the saw-toothed chip in 1954, obtained in turning of a titanium alloy, when this work material was initially being considered as a structural material. In this micrograph, presented by Shaw (Fig. 3(a) in [45]), however, no severe plastic deformation can be observed in the regions adjacent to the cracks formed between the chip elements. Actually, the same can be said about other micrographs presented in this picture for continuous fragmentary chip where the heavily deformed chip contact layer, normally found in this kind of the chip, is not seen. Nakayama studied the metal cutting process using a highly cold-worked brass as the work material at very low cutting speeds and suggested [100] a theory of saw-toothed chip formation. The model used to describe this theory is shown in Fig. 1.41(a).

Cutting force (db ref 5000N)

56

Tribology of Metal Cutting

20

0

Feed f = 0.12 mm/rev

−20 −40

(a)

−60 −80 −100 −120 0

200

400

600

800

1000

1200

1400

1600

1800

Cutting force (db ref 5000N)

Frequency (Hz)

20

Feed f = 0.12 mm/rev

0 −20 −40

(b)

−60 −80 −100 −120 0

200

400

600

800

1000

1200

1400

1600

1800

Cutting force (db ref 5000N)

Frequency (Hz) 20

0

Feed f = 0.12 mm/rev

−20 −40

(c)

−60 −80 −100 −120 0

200

400

600

800

1000

1200

1400

1600

1800

Frequency (Hz)

Fig. 1.39. Power spectra for the cutting force signal. Work materials: (a) AISI steel 303, (b) AISI steel 4340 and (c) AISI steel 1045 (after Astakhov [25]).

Generalized Model of Chip Formation

57

f, KHz 4.00 2.00 1.00 0.40 0.20

1018 steel 1045 steel

0.10

Cr-Ni-Mn Alloy 303 steel

0.05 0.05

0.10

0.40

1.00

n, m/s

2.00

Fig. 1.40. Effect of cutting speed on the frequency of chip formation (after Astakhov [18]).

B

A 2

Crack

Rc

1

B

A

Rc

1

2

O

O 2

1

(a) 1 B C

A

A

B Rc

B' 2

C

B' 3

3

1 Rc

2

O

O 4

3

Smin = 0 Smax t max Smax

(b)

Smin = 0

Fig. 1.41. Model of chip formation of the segmental chip suggested by Nakayama: (a) system consideration and (b) state of stress at point B.

58

Tribology of Metal Cutting

According to this model, the chip formation process is cyclic (periodic). The following phases can be distinguished in this model: • Phase 1 (Fig. 1.41(a)) illustrates the state when chip element 1 has almost completed its formation and the formation of the next chip element 2 has just started (according to the model, the formation of two-chip fragments takes place in each cycle). The formation of chip element 2 begins with a further rise of the workpiece free surface at point A. • Phase 2 begins when segment AB becomes parallel to the direction of the cutting force. Then, a shear crack is initiated at point B heading downward along the shear plane to the cutting edge represented by point O. The state of the stress achieved at this phase is shown in Fig. 1.41(b). The crack then develops until the crack-arresting normal stress becomes high enough to cease crack propagation. • Phase 3 begins when the chip element 2 starts to glide outward like a friction slider along the cracked surface until the next crack is formed at point C. • Phase 4 is the same as Phase 1. Chip element 2 has almost finished its formation and the formation of the next chip element 3 has just started. In the author’s opinion, the results obtained in Nakayama’s tests are rather methodological than application oriented because: • Chip formation processes at low and high (normal) cutting speeds are entirely different for the same cutting regime, work material, tool material and geometry. Zorev [29] conducted the comparison of chip formation at low (Chapter 2 in [29]) and high cutting speeds (Chapter 3 in [29]) and thus proved and concluded the above theory. He demonstrated that a work material that readily cracks at very low cutting speed (similar to that used in Nakayama’s tests) would not do so at a higher cutting speed (for example, Figs. 38 and 139(a) in Zorev’s book [29]). • The state of stress shown in Fig. 1.41(b) corresponds to pure compression. Because the work material is assumed to be of highly cold-worked material (brittle), the crack may not form in the direction of the maximum shear stress because the work material has already exhausted its ability to deform plastically. • The deformed chip structure presented by Nakayama does not support the model discussed because there is no distortion of the grains along the direction of crack formation. If, as suggested by the model, a crack formed at the workpiece free surface does not run through the whole chip towards the cutting edge due to high arresting stresses, only a part of the chip cross section slides as a glide and the other part should be deformed plastically to a great extent. In the micrograph presented by Nakayama, however, no traces of plastic deformation are observed. The most essential findings made by Nakayama, about crack initiation at the free surface of the partially formed chip was experimentally confirmed by Kishawy and Elbestawi [101] in their study of chip morphology when machining a hardened steel (in both orthogonal cutting on tubes and oblique cutting) at a cutting speed of ν = 160 m/min with a metalloceramic tool TNG having a negative rake angle γ = −6◦. They also found that this crack develops without noticeable deformation of the workpiece free surface, as was

Generalized Model of Chip Formation

59

suggested by Nakayama at low cutting speeds. The model of chip formation used by Kishawy and Elbestawi [101] (Fig. 1.42), was developed by Elbestawi, Srivastawa and El-Wardany, assuming that the compressive stresses in front of the cutting edge lead to crack formation at the free surface owing to the brittleness of the work material [102]. According to this model, a crack initiates at the workpiece free surface (point B) without any noticeable plastic deformation (raise of AB) and then propagates toward the tool. However, the propagation ceases before this crack reaches the cutting edge (point C), where severe plastic deformation exists due to the high compressive stress and temperature originated from the cutting edge. The crack DC formed then serves as a sliding plane for the fractured material enclosed between the tool rake face and this crack. This part (region ABCD in Fig. 1.42(a)) of the layer being removed from segment 1 of the chip shown in Fig. 1.42(b). Further tool advance leads to the extrusion of region CDO into segment 2 of the chip formed (Fig. 1.42(b)). However, the experimental part of study by Kishawy and Elbestawi [101] did not fully support the model discussed. Particularly, the microhardness test showed the presence of significant plastic deformation in chip segment 1. At low cutting feeds, this deformation is concentrated at the lower part of this segment, while the upper part is found to be more deformed at high feeds. It cannot happen if the fracture and deformation of the layer being removed take place according to the model shown in Fig. 1.42(a). Analyzing segmental chip formation, one may conclude that it takes place in machining under rather specific conditions when: • Work material has special properties: hardened, heat treated, high strength – both ultimate and yield (for example, titanium alloys), low thermal conductivity, etc. • Uncut chip thickness is rather small and/or variable along the cutting edge. For example, Vyas and Shaw [45] used round cutting edge in their hard turning tests. Although the variable chip thickness causes different cutting conditions for different sections perpendicular to the cutting edge, they constructed their model using the plane strain assumption.

Upper part B

Lower part

−g

A D C O

Segment 1 Segment 2

(a)

(b)

Fig. 1.42. (a) Model of chip formation of the segmental chip suggested by Elbestawi, Srivastawa and El-Wardany, and (b) chip fragment produced according to this model.

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• Cutting speed is very high for a given work material so the localized deformation in chip formation is characterized by three sequential events [95,103]: elastic deformation, plastic deformation (hardening and softening), and finally local failure and shearing. • Machining system is not dynamically stable [104]. A detailed analysis of the multiple publications on the subject allows the author to conclude that the segmental chips are often formed when machining difficult-to-machine materials at elevated cutting speeds, as shown in Fig. 1.28(d) and in Fig. 1.43. Low thermal conductivity, small difference between the ultimate and yield strength, high hardness enhance the formation of the elemental chip. However, the mechanism of its formation is not different from that of the formation of the saw-toothed chip (Fig. 1.32). Multiple studies conducted by Jawahir (for example, [13,14,82]) showed that the elemental chip often formed as a part of the “normal” saw-toothed chip even for “usual” work materials like AISI steel 1045 machined at cutting speed ν = 150 m/ min, cutting feed f = 0.5 mm/rev (Fig. 11 in [14]). The segmental chip should not be mixed with unstable chip having similar appearance. In the author’s opinion, the variation of the cutting force being the major and most powerful source, causes and thus creates vibrations in the machining system, not vice versa as concluded by Komanduri [104].

1.10 Applicability and Significance of Chip Formation Models The rapid progress in the development of cutting tool materials including coatings and in the design, manufacturing and application of indexable cutting inserts having various shapes of the rake surface brought significant changes in the cutting processes over the last 10 years. Moreover, wide use of specialized Computer Numerical Control (CNC) and multi-axis high-precision machines having rigid structures changed the methodology of tool design and application. As a result, one may wonder if the “classical” representation of cutting process by models of chip formation suitable for orthogonal cutting is still of any assistance to tool and process designers. In other words, a simple question is to be answered: what useful information that can be obtained knowing and understanding the different chip formation models? To be able to answer this challenging question, one should know how to correlate a real cutting process to that considered by orthogonal cutting models. To do that, certain strict definitions of the basic terms have to be clarified. These are discussed in Appendix A. Once these are clearly established, useful information about the contact stresses, temperatures, energy partition in the cutting system and many other important aspects of the cutting process can be obtained from such modeling. This information is to be directly used in the cutting wedge design, engineering, and choice of tool materials and coatings, selection of cutting fluids, and methods of its proper application and the determination of the stability of the cutting process. Moreover, this information is of prime importance when one tries to correlate the input parameters of the cutting process with its outputs as needed, quality of the machined parts including the machining residual stresses, productivity, etc.

Generalized Model of Chip Formation

61

Zone A

Zone B

(a)

Zone A

Zone B

(b) Zone A

Zone B

(c) Fig. 1.43. Non-uniform deformation of chip fragments in machining work material 4 (Fig. 2.27(d)): (a) cutting speed ν = 150 m/min, heavily deformed part (Zone A) occupies approximately 62% of the chip segment area. Its hardness is 756 HV, the hardness of the chip in Zone B is 632 HV; (b) cutting speed ν = 300 m/min, heavily deformed part (Zone A) occupies approximately 40% of the chip segment area. Its hardness is 742 HV, the hardness of the chip in Zone B is 640 HV; (c) cutting speed ν = 1500 m/min, heavily deformed part (Zone A) occupies approximately 33% of the chip segment area. Its hardness is 720 HV, the hardness of the chip in Zone B is 618 HV (Courtesy of Prof. S. Ekinoviˆc).

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Another important aspect is the reliable chip control, which is of great importance in automated machining. Knowing a particular chip type for a given set of machining conditions, one should be able to select the optimum type of chipbreaking techniques to control the shape and length of chip pieces suitable for transportation from the machining zone.

References [1] Usui, E., Shirakashi, T., Mechanics of metal cutting – from “description” to “predictive” theory. In On the Art of Cutting Metals – 75 Years Later, Production Engineering Division (PED), ASME, Phoenix, USA, 1982. [2] Usui, E., Progress of “predictive” theories in metal cutting, JSME International Journal, 31 (1988), 363–369. [3] Armarego, E.J.A., Predictive modeling of machining operations – a means of bridging the gap between the theory and practice – a keynote paper. In The 13th Symposium on Engineering Applications of Mechanics, CMSE, Hamilton, ON, Canada, 1996. [4] Endres, W.J., Devor, R.E., Kapoor, S.G., A dual-mechanism approach to the prediction of machining forces, Part 1: model development, ASME Journal of Engineering for Industry, 117 (1995), 526–533. [5] Kopac, J., Dolinsek, S., Advantages of experimental research over theoretical models in the field of metal cutting, Experimental Techniques, 20 (1996), 24–28. [6] Armarego, E.J., Brown, R.H., The Machining of Metals, Prentice Hall, New Jersey, USA, 1969. [7] Shaw, M.C., Metal Cutting Principles, Second Edition. Oxford University Press, Oxford, 2005. [8] Modeling and Optimization Packages AdvantEdge 4.6, Third Wave Systems, Minneapolis, MN, USA, 2006 (www.thirdwavesys.com/). [9] DeGarmo, E.P., Black, J.T., Kohser, R.A., Materials and Processes in Manufacturing, Nineth Edition. John Wiley & Sons, New York, 2003. [10] Kalpakjian, S., Schmid, S.R., Manufacturing Engineering and Technology, Prentice Hall, New Jersey, USA, 2001. [11] Gorczyca, F.Y., Application of Metal Cutting Theory, Industrial Press, New York, 1987. [12] Shaw, M.C., Metal Cutting Principles, Oxford Science Publications, Oxford, 1984. [13] Jawahir, I.S., Balaji, A.K., Stevenson, R., van Luttervelt, C.A., Towards predictive modeling and optimization of machining operations. In Manufacturing Science and Engineering. Proc. 1997 ASME International Mechanical Engineering Congress and Exposition, Dallas, TX, 1997. [14] Jawahir, I.S., Zhang, J.P., An analysis of chip curl development, chip deformation and chip breaking in orthogonal machining, Transactions of NAMRI/SME, XXIII (1995), 109–114. [15] Fang, N., Jawahir, I.S., Oxley, P.L.B., A universal slip-line field model with nonunique solutions for machining with curled chip formation and a restricted contact tool, International Journal of Mechanical Science, 43 (2001), 557–580.

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[16] Fang, N., Jawahir, I.S., Analytical predictions and experimental validation of cutting force ratio, chip thickness, and chip back-flow angle in restricted contact machining using the universal slip-line model, International Journal of Machine Tools and Manufacture, 42 (2002), 681–694. [17] Fang, N., Jawahir, I.S, Oxley, P.L.B., A universal slip-line model with non-unique solutions for machining with curled chip formation and a restricted contact tool, International Journal of Mechanical Sciences, 43 (2001), 557–580. [18] Finnie, I., Review of the metal-cutting analysis of the past hundred years, Mechanical Engineering, 78 (1956), 715–721. [19] Piispanen, V., Lastunmuodostumisen teoriaa, Teknillinen Aikakauslehti, 27 (1937), 315–322. [20] Piispanen, V., Theory of formation of metal chips, Journal of Applied Physics, 19 (1948), 876–881. [21] Oxley, P.L.B., Mechanics of Machining: An Analytical Approach to Assessing Machinability, John Wiley & Sons, New York, USA, 1989. [22] Time, I., Resistance of Metals and Wood to Cutting (in Russian), Dermacow Press House, St. Petersburg, Russia, 1870. [23] Tresca, H., Mémores sur le Rabotage des Métaux, Bulletin de la Société d’Encouragement pour l’Industrie Nationale, 15 (1873), 585–685. [24] Time, I., Memore sur le Rabotage de Métaux, Industrial Chamber St. Petersburg, Russia, 1877. [25] Astakhov, V.P., Metal Cutting Mechanics, CRC Press, Boca Raton, USA, 1998. [26] Zvorykin, K.A., On the force and energy needed to separate the chip from the workpiece (in Russian), Tekhicheskii Sbornik i Vestnic Promyslinosty, 123 (1896), 57–96. [27] Boston, O.W., A Bibliography on Cutting of Metals, ASME, New York, 1945. [28] Briks, A.A., Metal Cutting (in Russian), Dermakow Publishing House, St. Petersburg, 1896. [29] Zorev, N.N., Metal Cutting Mechanics, Pergamon Press, Oxford, 1966. [30] Johnson, W., Mellor, P.B., Engineering Plasticity, van Nostrand Reinhold Company, London, Inglaterra, 1973. [31] Palmer, W.B., Oxley, P.L.B., Mechanics of metal cutting, Proceedings of the Institution of Mechanical Engineers, 173 (1959), 557–580. [32] Kudo, H., Some new slip-line solutions for two-dimensional steady-state machining, International Journal of Mechanical Sciences, 7 (1965), 43–55. [33] Okushima, K., Hitomi, K., An analysis of the mechanism of orthogonal cutting and its application to discontinuous chip formation, ASME Journal of Engineering for Industry, 83 (1961), 545–556. [34] Ernst, H., Merchant, M.E., Chip formation, friction and high quality machined surfaces, Surface Treatment of Metals, ASM, 29 (1941), 299–378. [35] Merchant, M.E., Mechanics of the metal cutting process. I. Orthogonal cutting and a type 2 chip, Journal of Applied Physics, 16 (1945), 267–275.

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[36] Lee, E.H., Shaffer, B.W., The theory of plasticity applied to a problem of machining, Journal of Applied Mechanics, 18 (1951), 405–413. [37] Reuleaux, F., Über den taylor whiteschen werkzeugstahl verein sur berforderung des gewerbefleissen in preussen, Sitzungsberichete, 79 (1900), 179–220. [38] Atkins, A.G., Modeling metal cutting using modern ductile fracture mechanics: qualitative explanations for some longstanding problems, International Journal of Mechanical Sciences, 45 (2003), 373–396. [39] DeGamo, E.P., Black, J.T., Kohser, R.A., Materials and Processing in Manufacturing, Macmillan, New York, 1988. [40] Astakhov, V.P., Osman, M.O.M., Hayajneh, M.T., Re-evaluation of the basic mechanics of orthogonal cutting: velocity diagram, virtual work equation and upperbound theorem, International Journal of Machine Tools and Manufacture, 41 (2001), 393–418. [41] Black, J.T., Huang, J.M., Shear strain model in metal cutting, Manufacturing Science and Engineering, MED-Vol. 21 (1995), 283-302. [42] DeGarmo, E.P., Black, J.T., Kohser, R.A., Materials and Processes in Manufacturing, Prentice Hall, Upper Saddle River, NJ, 1997. [43] Altintas, Y., Manufacturing Automation. Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design, Cambridge University Press, Cambridge, 2000. [44] Stephenson, D.A., Agapiou, J.S., Metal Cutting Theory and Practice, Marcel Dekker, New York, 1996. [45] Vyas, A., Shaw, M.C., Mechanism of saw-tooth chip formation in metal cutting, ASME Journal of Manufacturing Science and Engineering, 121 (1999), 163–172. [46] Field, J.E., Walley, S.M., Proud, W.G., Goldrein, H.T., Siviour, C.R., Review of experimental techniques for high rate deformation and shock studies, International Journal of Impact Engineering, 30 (2004), 725–775. [47] Rohr, I., Nahme, H., Thoma, K., Material characterization and constitutive modelling of ductile high strength steel for a wide range of strain rates, International Journal of Impact Engineering, 31 (2005), 401–433. [48] Tönshoff, H.K., Amor, R.B., Andrae, P., Chip formation in high speed cutting (HSC), SME Paper MR99–253, SME, Dearborn, MI, 1999. [49] Astakhov, V.P., Shvets, S., The assessment of plastic deformation in metal cutting, Journal of Materials Processing Technology, 146 (2004), 193–202. [50] Payton, L.N., Black, J.T., Low speed orthogonal machining of cupper with hardness gradient, SME Technical Paper MR01-266, 2001, pp. 1–8. [51] Merchant, M.E., Basic mechanics of metal cutting process, Journal of Applied Mechanics, 11 (1944), A168–A175. [52] Astakhov, V.P., Outeiro, J.C., Modeling of the contact stress distribution at the tool–chip interface. In Proceeding of the 7th CIRP International Workshop on Modeling of Machining Operations, ENSAM, Cluny, France, 2004.

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[53] Poletica, M.F., Contact Loads on Tool Interfaces (in Russian), Machinostroenie, Moscow, 1969. [54] Loladze, T.N., Strength and Wear of Cutting Tools (in Russian), Mashgiz, Moscow, 1958. [55] Childs, T.H.C., Maekawa, K., Obikawa, T., Yamane, Y., Metal Machining. Theory and Application, Arnold, London, 2000. [56] Kronenberg, M., Machining Science and Application. Theory and Practice for Operation and Development of Machining Processes, Pergamon Press, Oxford, 1966. [57] Hill, R., The mechanism of machining: a new approach, Journal of the Mechanics and Physics of Solids, 3 (1954), 47–53. [58] Rubenstein, S., A note concerning the inadmissibility of applying of minimum work principle to metal cutting, ASME Journal of Engineering for Industry, 105 (1983), 294–296. [59] Dewhurst, W., On the non-uniqueness of the machining process, Proceedings of the Royal Society of London, A, 360 (1978), 587–609. [60] Shaw, M.C., Metal Cutting Principles, Second Edition. Oxford University Press, Oxford, 2004. [61] Ernst, H., Physics of Metal Cutting, The Cincinnati Milling Machine Co., Cincinnati, OH, USA, 1938. [62] Trent, E.M., Wright, P.K., Metal Cutting, Butterworth-Heinemann, Boston, 2000. [63] Trent, E.M., Metal cutting and the tribology of seizure. Part 1. Seizure in metal cutting, Wear, 128 (1988), 29–37. [64] Astakhov, V.P., A treatise on material characterization in the metal cutting process. Part 1: A novel approach and experimental verification, Journal of Materials Processing Technology, 96 (1999), 22–33. [65] Outeiro, J.C., Application of Recent Metal Cutting Approaches to the Study of the Machining Residual Stresses, in Department of Mechanical Engineering, University of Coimbra, Coimbra, 2003, p. 340. [66] Pugh, H.L.D., Mechanics of metal cutting process. In Proc. IME Conf. Tech. Eng. Manufacture, London, 1958. [67] Chisholm, A.W.J., A review of some basic research on the machining of metals. In Proc. IME Conf. Tech. Eng. Manufacture, London, 1958. [68] Bailey, J.A., Boothrouyd, G., Critical review of some previous work on the mechanics of the metal-cutting process, ASME Journal of Engineering for Industry, 90 (1969), 54–62. [69] Creveling, J.H., Jordon, T.F., Thomsen, E.G., Some studies on angle relationship in metal cutting, ASME Journal of Applied Mechanics, 79 (1958), 127–138. [70] Zorev, N.N., Results of work in the field of the mechanics of the metal cutting process. In Proc. IME Conf. Tech. Eng. Manufacture, London, 1958. [71] Hill, R., The Mathematical Theory of Plasticity, Oxford University Press, London, 1950. [72] Hill, R., The mechanics of machining: a new approach, Journal of the Mechanics and Physics of Solids, 3 (1954), 47–53.

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[73] Atkins, A.G., Mai, Y.W., Elastic and Plastic Fracture: Metals, Polymers. Ceramics, Composites, Biological Materials, John Wiley & Sons, New York, 1985. [74] Astakhov, V.P., Chapter 9: Tribology of metal cutting, in Mechanical Tribology. Material Characterization and Application, G.T.a.H. Liang, Editor. Marcel Dekker, New York, 2004, pp. 307–346. [75] Boothroyd, G., Knight, W.A., Fundamentals of Machining and Machine Tools, Second Edition. Marcel Dekker, New York, 1989. [76] Astakhov, V.P., The assessment of cutting tool wear, International Journal of Machine Tools and Manufacture, 44 (2004), 637–647. [77] Eleftherion, E., Bates, C.E., Effect of inoculation on machinability of grey cast iron, ASF Transactions, 122 (1999), 659–669. [78] Garry, J.R.C., Wright, I.P., The Cutting Strength of Cryogenic Water, Ice Planetary Science Research Institute, Open University, England, 2000. [79] Nakayama, K., Arai, M., Comprehensive chip form classification based on the cutting mechanism, Annals of the CIRP, 71, 1992 (1992), 71–74. [80] Nakayama, K., Chip Control in Metal Cutting, Bulletin of Japanese Society of Precision Engineering, 18 (1984), 97–103. [81] Dieter, G., Mechanical Metallurgy, McGraw-Hill, New York, 1976. [82] Jawahir, I.S., van Luttervelt, C.A., Recent Developments in Chip Control Research and Applications, Annals of the CIRP, 42 (1993), 659–693. [83] Astakhov, V.P., Shvets, S.V., A system concept in metal cutting, Journal of Materials Processing Technology, 79 (1998), 189–199. [84] Touret, R., The Performance of Metal Cutting Tools, American Society for Metals, Heston, 1957. [85] Slater, R.A.C., Engineering Plasticity: Theory and Application to Metal Forming Processes, The Macmillan Press Ltd., London, 1977. [86] Abuladze, N.G., The tool–chip interface: determination of the contact length and properties (in Russian), in Machinability of Heat Resistant and Titanium Alloys. Kyibashev Regional Publ. House, Kyibashev, Russia, 1962, pp. 87–96. [87] Astakhov, V.P., Svets, S.V., Osman, M.O.M., Chip structure classification based on mechanics of its formation, Journal of Materials Processing Technology, 71 (1997), 247–257. [88] Astakhov, V.P., A treatise on material characterization in the metal cutting process. Part 2: Cutting as the fracture of workpiece material, Journal of Materials Processing Technology, 96 (1999), 34–41. [89] Osman, M.O.M., Sankar, T.S., Short-time acceptance test for machine tools based on the random nature of the cutting forces, ASME Journal of Engineering for Industry, 94 (1972), 1020–1025. [90] Chandrashekhar, S., Sankar, T.S., Osman, M.O.M., An experimental investigation for the stochastic modeling of the resultant force system in BTA deep-hole machining, International Journal of Production Research, 23 (1985), 657–669.

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[91] Chandrashekhar, S., Sankar, T.S., Osman, M.O.M., A stochastic characterization of the tool-workpiece system in BTA deep hole machining. Part 1: Mathematical modeling and analysis, Adv. Manuf. Process. J., 2 (1987), 37–48. [92] Mills, B., Redford, A.H., Machinability of Engineering Materials, Applied Science Publishers, London, 1983. [93] Trent, E.M., Metal Cutting, Butterworth Heinemann, London, Inglaterra, 1991. [94] Ekinovic, S., Dolinsek, S., Brdarevic, S., Kopac, J., Chip formation process and some particularities of high-speed milling of steel materials. In Trends in the Development of Machinery and Associated Technology, TMT 2002, B&H, Neum, 2002. [95] Tonshoff, H.K., Amor, P.B., Amdrae, P., Chip formation in high speed cutting (HSC), SME Paper MR99–253, 1999. [96] Talantov, N.V., Unstable plastic deformation and self-exited vibrations in metal cutting (in Russian) in Metalworking Technology and Automatization of Manufacturing Processes, N.V. Talantov, Editor. VPI, Volgograd, 1984, pp. 37–41. [97] Lindberg, B., Lindstrom, B., Measurements of the segmentation frequency in the chip formation process, Annals of the CIRP, 32 (1983), 17–20. [98] Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T., Power spectra estimation using the FFT, in Numerical Recipes in FORTRAN: The Art of Scientific Computing, Second Edition. Cambridge University Press, Cambridge, UK, 1992, pp. 542–551. [99] Astakhov, V.P., Shvets, S.V., A novel approach to operating force evaluation in high strain rate metal-deforming technological processes, Journal of the Materials Processing Technology, 117 (2001), 226–237. [100] Nakayama, K., Formation of saw tooth chips. In International Conference on Production Engineering, Tokyo, 1974. [101] Kishawy, M.A., Elbestawi, M.A., Effect of process parameters on chip morphology when machining hardened steel. In Int. Mech. Eng. Congress and Exposition, Manufacturing Science and Technology, ASME, Dallas, Texas, 1999. [102] Elbestawi, M.A., Srivastawa, S.A.K., El-Wardany, T.I., Model for chip formation during machining of hardened steel, Annals of the CIRP, 45 (1996), 71–76. [103] Grady, D.E., Kipp, M.E., The growth of unstable thermoplastic shear with application to steady-wave shock compression in solids, Journal of Mechanics and Physics of Solids, 35 (1987), 95–118. [104] Komanduri, R., Brown, R.H., On the mechanism of chip segmentation in machining, ASME Journal of Engineering for Industry, 103 (1981), 33–51.

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CHAPTER 2

Energy Partition in the Cutting System

2.1 Introduction As pointed out by Bhushan [1], tribology is the art of applying operational analysis to the problems of great economic significance. Surface interactions in tribological interfaces are highly complex, and their understanding requires knowledge of various disciplines including physics, chemistry, applied mathematics, solid mechanics, fluid mechanics, thermodynamics, heat transfer, materials science, rheology, lubrication, machine design, performance and reliability. Understanding the tribological interactions discussed can only be possible if the energy involved is known, because any interaction should be thought of as a kind of energy exchange. The amount of energy transmitted through a tribological interface defines to a large extent the actual occurrence of various physical and chemical processes that might happen at this interface because any of these processes requires a certain level of energy to trigger and maintain this process. As discussed in Chapter 1, the cutting process takes place in the cutting system consisting of the cutting tool, workpiece and chip [2]. The major system properties, such as the system time and the dynamic interaction between the system components were used to reveal the essential characteristics of the cutting process. Besides, it is necessary to point out that the cutting system is a sub-system of a more general system defined as the machining system. The machining system includes a number of sub-systems such as the machine tool, the control system, the coolant supply system, the loading–unloading system, etc. The main objective of the machining system is to provide optimum conditions for the performance of the cutting system because the quality of the machine part and the efficiency of machining are determined by the performance of the cutting edge of the cutting tool(s). Therefore, the system interactions between the sub-systems of the machining system and the cutting system should be established, optimized and maintained to achieve optimum performance of the cutting system. The most general level of such interactions is their energy levels, so that these interactions can be thought of as the energy flows in the machining system. 69

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This chapter clarifies the energy aspects of the metal cutting tribology. It considers a complete model of energy partition and flows in the metal cutting system for the first time. It introduces the concept of physical efficiency of the cutting system and presents a simple way for its determination. It also reveals the significance of the chip compression ratio in the study and optimization of the cutting processes. It discusses distinctive ways of increasing the physical efficiency of the cutting system.

2.2 Energy Flows in the Cutting System Generalization of the theoretical and experimental results on the performance of the cutting system allows the graphical representation of energy flows and conversions in the cutting system, as shown in Fig. 2.1 [3]. The total energy entering the cutting system, Ucs is a part of the energy produced by the drive motor, Uem . Obviously that Ucs = Uem ηpt ,

(2.1)

where ηpt is the efficiency of the power train that connects the cutting system and the drive motor of the machine tool.

Ucs =Uem.hpt QeT

TOOL WTc+WTb

UT

Q1 Qta

Qtg Wt g

Wta Q3

Q2 WORKPIECE

Qtw Qw

Qtc Qfw

Q4

Qwr Uw

Qwf

Q6

Qfc

Wf

Q5

Qew

Wcc+Wcb

Uc

Qec

Uf CHIP

Fig. 2.1. Graphical representation of energy flows in the metal cutting system (after Astakhov [3]).

Energy Partition in the Cutting System

71

Ideally, if there is no energy loss in the cutting system, the energy transmitted through the cutting tool having the cutting tool energy UT to the chip with the chip energy Uc and then to the chip formation zone, having the deformation energy Wf is equal to the energy needed for the separation of the layer being removed, Uf [4], i.e. Ucs = UT = Uc = Wf = Uf . In real cutting systems, however, the energy losses occur due to elastic and plastic deformations of their components as well as friction losses during various interactions of these components. These losses do not correlate directly with the separation of the layer being removed. These energy losses are converted into heat (or the thermal energy), which, in turn, affect these losses even further.

2.2.1 Cutting tool Consider the energy flows in the components of the cutting system. The first component is the cutting tool. According to the energy conservation law, the work done over compression (WTc ) and bending (WTb ) of the cutting tool transforms into its potential energy (UT ) and also is partially spent on internal friction during deformations, which results in heat generation (Q1 ). Since the cutting tool is normally subjected only to elastic deformation, Q1 is small. However, when the cutting tool is not rigid and/or when it vibrates with an appreciable amplitude during machining, the share of this thermal energy may become significant. The potential energy UT is then spent as the work done by the frictional forces on the tool–chip and tool–workpiece interfaces, Wtα and Wtγ , respectively, and as the work done over the chip. The works of the frictional forces, Wtα and Wtγ , convert into the thermal energies, Q2 and Q3 , respectively. The thermal energy Q3 is generated at the tool–chip interface. It is then conducted into the tool, Qtγ , and into the chip, Qtc . The portions of heat conducted into the tool and the chip are in inverse proportion to their thermal resistances. Similarly, the thermal energy generated at the tool flank(s)– workpiece interface (Q2 ) is then distributed between the tool (Qtα ) and the workpiece (Qtw ) in inverse proportion to their thermal resistances. In the current consideration, the notion of thermal resistance is used as being more general compared to simple thermoconductivity because the cutting system is so dynamic that a number of system parameters contribute to the thermal resistances of its components, which are in relative motion with respect to each other. Because the directions of heat flow are as shown in Fig. 2.1, the tool contact surfaces (the tool–chip and tool–workpiece interfaces) always have higher temperatures than the rest of the cutting tool. The temperature gradient decreases with the distance from the tool rake face. As a result, the thermal energy flows in the direction of the rake face until the temperature gradient becomes zero. The same can be said about the heat flow from the tool flank contact surface. The exception is a small region adjacent to the cutting edge. Here, with the decreasing distance between the tool rake and flank surfaces, it can be assumed that the power of one heat source (acting at the rake or flank) exceeds that of the other. As such, heat would flow from the tool into the workpiece or the chip whichever heat source is weaker. In reality, however, it does not happen because the friction conditions on the tool rake and flank surfaces as well as their temperatures in the region adjacent to the cutting edge are balanced so that the temperature gradient is zero.

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Therefore, it can be concluded that the thermal energy flows only into the cutting tool from the tool–chip and tool–workpiece interfaces. The other surfaces of the cutting tool dissipate the thermal energy into the environment (QeT ). As explained in Chapter 1, the working part of the cutting tool is referred to as the cutting wedge. This is a part of the cutting tool enclosed between the tool rake and flank contact surfaces, which intersect to form the cutting edge. This cutting wedge is under the action of stresses applied on the tool–chip and tool–workpiece contact surfaces. Moreover, due to the thermal energy that flows into the cutting tool, this wedge has a high temperature. As a result, gradual exhaustion of the resource of the tool material takes place as explained in Chapter 4 [5,6]. Besides, high temperature due to this heat flow causes the plastic deformation of this wedge that appears as plastic lowering of the cutting edge. Such a deformation should be regarded as high-temperature creep (Chapter 4).

2.2.2 Chip The potential energy of the cutting tool is spent on the deformation of the chip. As discussed in Chapter 1, the chip serves as a lever to transmit the applied load into the chip formation zone [2,4,7]. A part of the work done by the compressive force and the bending moment, Wcc + Wcb over the chip, is dissipated in the chip converting into heat Q6 . The other part is the potential energy of the chip (Uc ) that makes its contribution Wf to the formation of the fracture energy (Uf ), which includes the energy needed for the formation of new surfaces. As discussed above, a part Qtc of the thermal energy Q3 generated at the tool–chip interface is also conducted into the chip. Besides, the chip also receives Qfc , a certain part of the thermal energy generated in the chip formation zone due to the plastic deformation of the layer being removed and heat due to fracture (Q4 ). The thermal energy (heat) Qtc from the chip interface flows into the chip primarily due to thermal conductivity and partially due to mass transfer because the chip moves over the tool–chip interface. Heat Qfc enters the chip due to mass transfer because the velocity of chip is normally higher than that of heat conduction in the chip [2]. In other words, the heat generated in the conversion of the layer being removed into the chip is transferred by the mass of the moving chip from the deformation zone, and not due to its thermal conductivity. As a result, the moving mass of the layer being removed is converted into the chip and the moving chip changes its energy along the tool–chip interface. This is true for each chip formation cycle. The chip temperature results in its higher plasticity and thus the energy losses in the transmission of the compressive force and bending moment into the chip formation zone increase which, in turn, increases Q6 . Additionally, some thermal energy (heat) Qen–c is released to the environment.

2.2.3 Workpiece It was demonstrated in Chapter 1 that the surface of the maximum combined stress, which eventually becomes the surface of fracture or chip separation, changes its position

Energy Partition in the Cutting System

73

within each chip formation cycle. Due to this fact, the energy of fracture of the layer being removed is distributed over a certain volume of the work material causing plastic deformation of this region, which normally extends below the surface that separates the layer being removed and the rest of the workpiece. Obviously, some part of the potential energy transferred into the chip formation zone is spent on the plastic deformation of this region (Uw ). It is confirmed experimentally and manifests itself by the cold working of the machined surface and results in machining the residual stress. As such, the thermal energy (heat) Q5 is released. Besides heat Q5 , heat Qtw from the tool flank–workpiece contact and heat Qfw from the chip formation zone are also supplied into the workpiece forming the total thermal energy Qw = Q5 + Qtw + Qfw . As conclusively proven by Astakhov [8], this thermal energy cannot increase the energy level in the fracturing of the layer being removed in the direction of the cutting speed because the velocity of heat conduction is much lower than the cutting speed. However, part of the thermal energy, transferred in the direction of the feed motion, can change this energy level. This is explained later in this chapter. A special case takes place in the machining of a workpiece of small diameter. As such, heat Qw , having been reflected many times by the outer surface of the workpiece, affects the energy level of its entire cross section, and thus is added to the energy of fracture Uf . Additionally, some heat, Qen−w , is released to the environment through convection, conduction and radiation.

2.3 Physical Efficiency of the Cutting System The word efficiency is a term used virtually everyday in a myriad of circumstances; thus, it needs to be clearly defined for any specific usage. This term, if used in the design of various technical systems, aims at obtaining the most effective engineering solutions at the expense of multidimensional optimization of system model and the assurance of the extremeness of one or several efficiency criteria in a wide range of operational modes. It is also used in the definition of optimal control laws of the complex technical systems for different operational modes; in the definition of optimum design solutions regarding the complex criterion as “efficiency−cost”; in the definition of the set of optimum engineering solutions, directed on efficiency increase of elements and of a technical system as a whole, in the comparative analysis of alternative optimum versions and substantiation of the final choice of technical solution. Nowadays the word efficiency is associated with process economy rather than with its physical nature. To distinguish efficiency as a techno-economic term and as a physically based entity, the term physical efficiency will be used in further considerations. Physical efficiency is defined in the classical way as a ratio of the useful energy provided by the cutting system to the total energy required by this system. As such, every change made in the cutting system would affect its efficiency in either way, hence the physical efficiency discussed can be thought of as an objective gauge to judge this change made in terms of the extent of improvement of the physical efficiency of the cutting system. Unfortunately, today, specialists in metal cutting at different levels (from the research

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lab to the shop floor) do not have such a gauge. Therefore, in the author’s opinion, a need is felt to develop such a practical and physically based objective gauge. It is obvious that not all the energy required by the cutting system (Ucs ) is spent for the separation of the layer being removed, i.e. for performing useful work Uf . As discussed above, a part of the energy spent in the cutting system is dissipated in the components of this system changing their properties, and in the environment. As a result, the cutting system consumes more energy than needed for the separation of the layer being removed. It is clear that better the organization of the components of the cutting system, smaller the difference between these two energies. Therefore, it appears to be reasonable to introduce the term of physical efficiency of the cutting system as the ratio (expressed as percentage) of the actual energy required for the separation of the layer being removed and the total energy spent in the cutting system ηcs =

Uf Ucs

(2.2)

The amount of energy required for separating a unit volume of the work material depends on many factors. However, as demonstrated in [9], the state of stress, strain rate and temperature are of prime importance. For a given cutting system, the system parameters, including system geometry and regime, uniquely define the stress and strain at fracture and thus Uf . In the design of practical cutting systems, achieving maximum efficiency may not be the ultimate goal. Rather, its optimization should be considered. This is because one needs to know the required time period of existence of the cutting system. In other words, for a given tool material, the cutting wedge should be so shaped and the cutting regime should be so selected that the tool wear rate is within the required limits. The latter condition may be at odds with the requirement of maximum efficiency. Moreover, a particular level of cutting system efficiency may be further corrected accounting for the required quality, including the integrity of the machined surface, productivity and other practical constraints. As discussed in [2], the specific energy of fracture of the layer being removed is determined under the state of stress in this layer as εf Uf =

σ(ε)dε,

(2.3)

0

where εf is the strain at fracture under the state of stress imposed by the cutting wedge. This strain is the major controlling parameter in metal cutting as it determines the energy spent in cutting, tool life, chip shape, and many other important characteristics and outcomes of the cutting process. The specific cutting energy required by the cutting

Energy Partition in the Cutting System

75

system can be determined as Ucs =

Pc τct , Vc

(2.4)

where Pc is the cutting power, τct is the machining time and Vc is the volume of the work material cut during time τct . Because Vc = fdw ντc , where f is the cutting feed (m/rev), dw is the depth of the cut (m), ν is the cutting speed (m/s); Pc = Fz ν, where Fz is the power component of the cutting force (N), the final expression for the physical efficiency of the cutting system can be written as fdw ηcs = Fz

εf σ(ε)dε

(2.5)

0

As follows from Eq. (2.5), the physical efficiency can be determined by knowing the  εf stress–strain curve of the work material ( 0 σ(ε)dε represents the area under the stress– strain curve of the work material), cutting regime (f and dw ), and by measuring the cutting force Fz . Although Eq. (2.5) can be directly used to determine the physical efficiency of the cutting system, there are at least two problems: • The first and foremost is that the cutting force cannot be measured with reasonable accuracy although this fact has never been honestly admitted by the specialists in this field. To appreciate the issue, one should consider the results of the joint program conducted by College International pour la Recherche en Productique–The International Academy for Production Engineering, http://www.cirp.net (CIRP) and National Institute of Standards and Technology (NIST) to measure the cutting force in the simplest case of orthogonal cutting [10]. The experiments were carefully prepared (the same batches of the workpiece (steel AISI 1045), tools, etc.) under the supervision of NIST and replicated at four different most advanced metal cutting laboratories in the world. Interestingly, although extraordinary care was taken while performing these experiments, there was significant variation (up to 50%) in the measured cutting force across these four laboratories. Obviously, such an accuracy is not acceptable in the calculations of the physical efficiency of the cutting system. • Second, many tool and cutting inserts manufacturers (not to mention manufacturing companies), do not have adequate dynamometric equipment to measure the cutting force and so it would be rather difficult to determine the cutting force for the calculations discussed. Many dynamometers used in this field are not properly calibrated because the known literature sources did not present proper experimental methodology for cutting force measurements using piezoelectric dynamometers. Therefore, to make practical calculations of the physical efficiency of the cutting system another approach has to be found.

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2.4 Determination of the Work of Plastic Deformation in Metal Cutting 2.4.1 The known measures of plastic deformation The concept of efficiency of the cutting system can be practical if there is a simple measure of the work of plastic deformation in metal cutting, which could be used even at the shop-floor level to estimate the efficiency of a given cutting process. The objective of this section is to present such a measure. As discussed earlier, in machining, the combined stress in the chip formation zone exceeds the strength of the work material (under a given state of stress imposed by the cutting tool), whereas other forming processes are performed by applying stress sufficient to achieve the well-known shear flow stress in the deformation zone. The ultimate objective of machining is to separate a certain layer from the rest of the workpiece with minimum possible plastic deformation and thus the energy consumption. Therefore, the energy spent on plastic deformation in machining must be considered as wasted. On the other hand, any other metal-deforming process, especially those involving high strains (e.g. deep drawing, extrusion) uses plastic deformation to accomplish the process. Parts are formed into useful shapes such as tubes, rods and sheets by displacing the material from one location to another [11]. Therefore, the better material, from the viewpoint of metal forming, should exhibit higher strain before the fracture occurs. It is understood that this is not the case in metal cutting where it is desired that the work material should have as small a strain at fracture as possible. Unfortunately, this does not follow from the traditional metal cutting theory which normally utilizes the shear strength or, at the best, the shear-flow stress (this term was specially invented for metal cutting to cover up the discrepancies between the theoretical and experimental results) to calculate the process parameters (cutting force, temperatures, contact characteristics) although the everyday machining practice shows that these parameters are lower in cutting brittle materials of higher strength. Historically, the chip compression ratio (CCR) (ζ) (or its reciprocal, the chip ratio), which is determined as the ratio of the length of cut (Ll ) to the corresponding length of the chip (Lc ) or the ratio of the chip thickness (t2 ) to the uncut chip thickness (t1 ), i.e. ζ=

Ll t2 = Lc t1

(2.6)

was introduced in the earlier studies on metal cutting as a measure of plastic deformation of the work material in its transformation into the chip [2,12] (Fig. 2.2). Due to the relative simplicity of its experimental determination, CCR was widely used in metal cutting studies as a quantitative measure of the total plastic deformation [12]. Numerous attempts have been made to establish analytically a relationship to predict CCR in terms of the fundamental variables of the cutting process. However, none of these attempts has produced results that match the experimentally obtained data for a reasonable variety of input conditions. Later, researchers abandoned this route in favor of the “modern” metal cutting approach in which this parameter is expected to be determined experimentally [12–20]. Because CCR competes with shear strain for the role of a measure of plastic

Energy Partition in the Cutting System

77

g Chip Lc

Cutting direction

t2

L1 Tool t1

Workpiece

Fig. 2.2. Scheme of chip deformation in cutting (after Astakhov [28]).

deformation encountered in metal cutting, it seems only logical to verify the justification of its usage as such a measure. As discussed in Chapter 1, Merchant [15] proposed the expression for the shear strain (Eq. (1.14)), which should be actually called the final shear strain [2]. As discussed in Chapter 1, when ζ = 1, the chip thickness is equal to the uncut chip thickness (Eq. (2.6)), the shear strain, calculated by Eq. (1.14) remains very significant. For example, when ζ = 1, the rake angle γ = −10◦ , Eq. (1.14) yields ε = 2.38; when ζ = 1, γ = 0◦ then ε = 2; when ζ = 1, γ = +10◦ then ε = 1.68. This reveals a contradiction; as CCR, considered to be a measure of plastic deformation, indicates that no plastic deformation occurs while the final shear strain remains significant. Moreover, if one compares the strains calculated using Eq. (1.14) with the standard mechanical characteristic of work materials, he can conclude that the strains in metal cutting significantly exceed (by 200– 1000%, depending on the rake angle) the strains at fracture of even very ductile materials [11]. To the best of the author’s knowledge, no study pointed out and/or explains this abnormality in the mechanical properties of work materials in machining. At this point, it is worthwhile to explain that the equation of final shear strain (Eq. (1.14)) was derived using purely geometrical considerations, i.e. it does not consider the change in internal energy of the chip due to the change in chip density, the increased dislocation concentration, or the stress imposed on the boundaries of the grains, etc., even though all of these increase the shear strength of the chip compared to the initial work material. Shear strain, according to Eq. (1.14), is defined only by the changes in the dimensions of a deformed body as compared to its original dimensions. As CCR indicates that there is no change in the dimensions, there is no “geometrical deformation,” so the strain should be equal to zero. However, this does not follow from the known equation for strain. Astakhov [2] pointed out that when properly measured, CCR directly reflects the final plastic deformation of the chip. Although this parameter was widely used in metal cutting tests of the past [12], it was always considered as a secondary parameter to provide

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qualitative support to certain conclusions. Since the real significance of this parameter has not been revealed, it was gradually abandoned in metal cutting studies because nobody could explain the meaning of the results obtained. For example, although Shaw dedicated a full chapter to the analysis of plastic deformation in metal cutting, in his book, this parameter is not even mentioned [9]. The same can be said about the books by Trent and Wright [18], Oxley [14] and Gorczyca [16]; and Altintas [19] just mentioned its definition in the consideration of the single-shear plane model; Childs et al. [20] mentioned this parameter as related to the friction coefficient at the tool–chip interface. Not a single modern study on metal cutting correlates this parameter with the amount of plastic deformation in metal cutting.

2.4.2 Work of plastic deformation The external forces applied, which result in the work done over the system, are not uniformly distributed over the system’s components. To define the action of an external force on the different regions of a body, the notion of stress is used. It is considered that if a body is subjected to a general system of body and surface forces, stresses of variable magnitude and direction are produced through the body. The distribution of these stresses must be such that the overall equilibrium of the body is maintained; furthermore, equilibrium of each element in the body must be maintained. Consider an infinitesimal element of parallelpiped form with its faces oriented parallel to the coordinate planes, as shown in Fig. 2.3. When the body and inertia forces are insignificant, the following three differential equations of force (stress) equilibrium are

z

sz

tzy

tzx

tyz

tyx

sy

txz

txy

sy

txy tyz sx x

sx

tyx

z

txz tzy

tzx

y

x

y

sz Fig. 2.3. Stresses acting on elemental free body.

Energy Partition in the Cutting System

79

obtained [2,21] ∂τxy ∂σx ∂τxz + + =0 ∂x ∂y ∂z

(2.7)

∂τxy ∂σy ∂τzy + + =0 ∂x ∂y ∂z

(2.8)

∂τyz ∂τxz ∂σz + + =0 ∂x ∂y ∂z

(2.9)

When a stress field applied to a body and, as a result, the relative position of its parts is changed, the body is deformed or strained. A deformed state in a point can be represented by the strain components if the projections ux , uy and uz , of the displacement of this point into the corresponding coordinate planes are known ex = γxy =

∂ux ∂x

ey =

∂uy ∂ux + ∂x ∂y

∂uy ∂y

ez =

γyz =

∂uz ∂z

∂uy ∂uz + ∂z ∂y

γzx =

∂uz ∂ux + , ∂x ∂z

(2.10)

where ex , ey and ez are the direct strains, γxy , γyz and γzx are the engineering shear strains. Using the generalized Hooke’s law, one can write the following relationship between the strains and stresses [21]   1  σx − νs σy + σz E   1  ez = σz − νs σx + σy E 2 ezx = (1 + νs ) τzx , E ex =

 1  σy − νs (σz + σx ) E 2 2 = (1 + νs ) τxy eyz = (1 + νs ) τyz E E

ey = exy

(2.11)

where E is the modulus of elasticity and νs is the Poisson’s ratio. The imbalanced external forces applied to a body cause its deformation and thus lead to the displacement of its points until the equilibrium is established. As such, a certain amount of energy is absorbed. This energy depends on the work done in displacement of all points of the body. Such work can be calculated by integrating the work per unit volume. The work per unit volume done in the displacement of each point of the body is calculated as the product of the generalized force acting on a point and the change of the generalized displacement of this point caused by this force. The von Mises’ stress [21]

1/ 2 2  2 1  2 2 2 σi = √ + τyz + τzx σx − σy + σy − σz + (σz − σx )2 + 6 τxy 2

(2.12)

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was considered as the generalized force and the equivalent strain √  1/ 2 2 ei = (ex − ey )2 + (ey − ez )2 + (ez − ex 2 + 6(e2xy + e2yz + e2zx ) 3

(2.13)

can be considered as the generalized displacement. Because the elementary work is dA = σi ei , the total work done over a volume V is then calculated as [2]  (2.14) A = σi ei dV V

As mentioned, CCR is used for the estimation of plastic deformation in experimental studies on the metal cutting process [2]. As such, the distribution of the mechanical energy over the cross section of the chip is assumed to be uniform. Using such an assumption, an engineering equation to calculate the energy spent in cutting can be obtained. If it is so, the CCR can be used to compare the power consumed in cutting of the same work material using different cutting processes. Moreover, the amount of power consumed, allows the comparison of machining different work materials. The engineering equation mentioned for the estimation of energy spent in the cutting process can be obtained using the assumption of homogeneous distribution of strain in Eqs. (2.12)–(2.14). To derive it, the xyz coordinate system is set so that the y axis is directed along the chip length (Lch ), the x axis is directed along the chip width (dw ) and the z axis is directed along its thickness (t2 ). As such, the following expressions for the components of the true strain along the coordinate axes introduced can be written accounting for the definition of CCR, ζ [2] εz = ln ζt

εx = ln ζb

εy = − ln ζL

(2.15)

As shown by Astakhov [2], in orthogonal cutting, the direction of the principal stress coincides with the coordinate system introduced. Then, Eq. (2.13) could be re-written accounting for Eq. (2.15) as √  1/ 2 2 (− ln ζL − ln ζt )2 + (ln ζt − ln ζb )2 + (ln ζb + ln ζL )2 εi = (2.16) 3 As shown in [2], if the chip parameters are properly measured in the orthogonal cutting test, then ζb = 1 and ζt = ζL = ζ, and therefore plane strain condition is the case in such a process. Hence, εi = 1.15 ln ζ

(2.17)

In the coordinate system considered, stress components σz and σy do not depend on the x coordinate (measured along chip width) and the σx component is determined as σx = 0.5(σz + σy )

(2.18)

Energy Partition in the Cutting System

81

Substituting these results in Eq. (2.15), one can obtain 2    2  2 1/ 2  1  + 0.5 σz + σy − σy + σy − σz σi = √ σz − 0.5 σz + σy 2

(2.19)

or after simplification σi = 0.87(σz − σy )

(2.20)

A true stress–strain curve is known as the flow curve because it gives the stress required to cause the metal to flow plastically to any given strain [11]. Although many attempts have been made to fit mathematical equations to this curve [22], the most common is a power expression of the form σ = Kεn ,

(2.21)

where K is the stress at ε = 1.0, n is the strain-hardening coefficient, and is the slope of a log–log plot of Eq. (2.21). Substitution of Eq. (2.21) into Eq. (2.20) yields



  σi = 0.87 Kεnz − Kεny = 0.87K εnz − εny = 0.87K (ln ζt )n − (ln ζL )n = 0.87K2(ln ζ)n = 1.74K(ln ζ)n

(2.22)

Because it was assumed that the chip has uniform deformation, the elementary work spent over plastic deformation of a unit volume of the work material is calculated as  Au = 0

εt

σdε =

k (1.15 lnζ)n+1 Kεn+1 t = n+1 n+1

(2.23)

The result obtained is of great significance to the experimental studies in metal cutting, because it correlates in a simple and physically grounded manner, the work of plastic deformation done in cutting with a measurable, post-process characteristic of the cutting process such as the CCR. Knowing the elementary work, the total work done by the external force applied to the tool is then calculated as A = Au νfdw τct

(2.24)

A series of cutting tests were carried out to compare the power consumption under different cutting conditions. All the tests were conducted using the same cutting feed f = 0.07 mm/rev and the depth of cut dw = 1 mm. Three different types of work material listed in Table 2.1 were used in the tests. For each work material, the influence of cutting speed on CCR was determined and the elementary work spent over plastic deformation of the work material was calculated using Eq. (2.23). The test results are shown in Fig. 2.4. As shown, although CCR is the greatest in the machining of copper and lowest in the machining of steel, the elementary work is the

82

Tribology of Metal Cutting Table 2.1. Work materials used in the tests. Material AISI steel E52100, HB280 (0.981.10% C, 1.45% Cr, 0.35% Mn) Copper (99.7%) Aluminum 1050–0, HB 21

K (GPa)

n

1.34

0.25

0.40 0.14

0.24 0.27

Au (GJ) 3

1

2 2 1 3 0

z 2 4 3

1 3 2

0

1

2

3

4

n (m/s)

Fig. 2.4. Influence of cutting speed on CCR and the work done in plastic deformation: 1 – AISI steel E52100, 2 – copper and 3 – aluminum 1050–0 (after Astakhov [28]).

greatest for steel. In other words, the energy per unit volume spent in the machining of steel is the greatest, which results in a much higher amount of heat generated and in more significant tool wear. This conclusion is supported by multiple facts known from the everyday practice of machining. It follows from Fig. 2.4 that CCR is a representative measure of the work of plastic deformation in metal cutting. For steel E52100, CCR varied within 67% under experimental conditions used in the test while the elementary work varied within 89%. For copper and aluminum, CCR varied within 60 and 55%, respectively, while the elementary work varied within 55 and 71%, respectively. The accuracy of estimation of the work done in plastic deformation can be improved if one accounts for the change in the parameters K and n (Eq. (2.23)) depending on the cutting speed (strain rate) and actual temperature in the chip formation zone. As such, two important issues should be accounted for.

Energy Partition in the Cutting System

83

• The first is that orthogonal metal cutting is essentially a cold-working process because the velocity of heat conduction is much lower than the cutting speed, and thus the thermal energy generated in the plastic deformation of the layer being removed does not affect the resistance of the work material to cutting ahead of the tool. In real cutting operations such as turning or drilling, only the residual heat from the previous position of the cutting tool may affect the temperature of the deformation zone at the current tool position. • The second issue concerns the strain rate in metal cutting. As considered by many specialists in the field, there is no need for special high strain rate tests to determine the value of constants K and n in Eq. (2.23). The method proposed for estimating the work of plastic deformation in metal cutting gives a new meaning to CCR. In the sense implied, it can be used as a prime parameter for the optimization of the metal cutting process because when considered together with the work of plastic deformation, it reveals the energy spent in cutting. Moreover, CCR is a post-process parameter and thus there are a number of simple though forgotten ways to measure this parameter accurately in metal cutting. Some simple methods of measuring CCR that can be used in shop floor for the optimization of practical cutting operations are discussed in Appendix B.

2.4.3 Influence of cutting speed It is well known that the cutting speed has the strongest influence on CCR [2,12]. Figure 2.5 shows an example of such an influence in the format commonly used in metal cutting studies [12]. The explanation of the shape of the graphs shown in Fig. 2.5 is still the same as it was 50 years ago when only the data obtained at low cutting speeds were available. The built-up edge is believed to be the prime factor affecting the shown dependencies [12]. The problem with this explanation is that the built-up edge does not exist at the speeds used to obtain data shown in Fig. 2.5. Therefore, another physically

z f = 0.12 mm/rev f = 0.48 mm/rev

f = 0.18 mm/rev f = 0.76 mm/rev

2.5

2.0

1.5 0

1

2

3

4

n

Fig. 2.5. Influence of cutting speed on CCR. Operation – longitudinal turning, workpiece diameter – 100 mm, work material – steel AISI 1045, tool material – carbide P20, tool cutting edge angle κr = 60◦ , normal rake angle γn = 7◦ and depth of cut dw = 3.5 mm (after Astakhov [28]).

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Tribology of Metal Cutting

sound explanation should be provided to help specialists to appreciate the meaning of CCR in the optimization of the metal cutting process. The cutting speed has the strongest influence on the energy distribution in the cutting system because it determines the intensity of the heat sources. Increasing the cutting speed leads to a decrease in the plastic deformation in the chip formation zone and, as a result, a lesser portion of the applied mechanical energy converts into heat (or thermal energy) in this zone so that the chip is “born” less hot. Simultaneously, however, the amount of heat generated at the tool–chip and tool–workpiece interfaces increase due to the increased chip velocity so that the chip, sliding over the tool rake face, receives more thermal energy. The total energy absorbed by the chip is equal to the sum of the thermal energies (heat) gained by the chip in its formation, i.e. during the plastic deformation of the layer being removed and that transferred into the chip from the tool–chip interface. The average temperature of the chip can be represented as [2,12] θch−aν = Cθ νxθ,

0 < xθ < 1

(2.25)

Multiple tests of different metallic materials showed [2,12] that if there were no metallurgical (chemical) transformations occurring on heating a material from temperature θ1 to θ2 , the elasticity modulus changes according to the following exponential equation Eθ2 = Eθ1 eαθ (θ1 −θ2 ) ,

(2.26)

where αθ is a constant for a given material. An increase in the thermal energy transferred to the chip with increasing cutting speed results in lowering the rigidity of the chip and its “effectiveness” as a lever to transmit the bending moment to the chip formation zone. As a result, the compressive stress takes a greater share in the combined stress in the chip formation zone. As such, the required external energy applied to the cutting system and that spent on plastic deformation of the layer to be removed, increases because this new state of stress in the deformation zone requires more energy for the separation of the layer being removed. In cutting, the external force is applied to the tool, and it is transmitted from its rake face into the chip formation zone through the chip. As such, certain energy losses occur in such a transmission. To estimate these losses, consider the work done by the force applied to the chip from the tool rake face. If lu designates the elementary length of the chip, then the work done over the chip by the force from the tool rake face consists of the work done by the bending moment and the compressive force dWch =

M 2 dlu Qdlu + , 2Ech Ich 2Ac Ech

(2.27)

where M is the bending moment (= SL) as per Fig. 1.20(d), Ech is the elasticity modulus of the material of the chip, Ich is the second moment or moment of inertia of the cross section of the chip, Q is the compressive force as per Fig. 1.20(d) and Ac is the crosssectional area of the chip.

Energy Partition in the Cutting System

85

If the elasticity modulus of the material of the chip tends to infinity, then it follows from Eq. (2.27) that dWch = 0, i.e. all the energy applied to the cutting tool is transmitted through the chip without losses. In reality, however, the modulus of elasticity is a finite value and, moreover, it decreases with the rise of temperature of the chip (Eq. (2.26)) so that part of the energy transmitted through the chip is spent on its deformation. As such, the work, of plastic deformation and fracture of the layer to be removed, done by the external force is calculated as dW = dWF − dWch

(2.28)

As discussed above, according to the energy theory of failure, a given volume of the work material fails when the critical internal energy is accumulated in this volume. As a result, dW can be considered as a constant for a given cutting system. According to Eq. (2.28), to keep dW constant when dWch increases, the energy supplied to the cutting tool by the external force (dWF ), should be increased. Flexural and compression rigidities of the chip, Ech Ich and Ac Ech , respectively, decrease with temperature according to Eq. (2.26). Therefore, an increase in the heat flow into the chip with the cutting speed leads to an increase in dWch , i.e. in increasing the energy needed for chip formation. The cutting speed affects the shape and dimensions of the chip formation zone [2,12] or the extent of the region of plastic deformation ahead of the tool. When the cutting speed increases, this region of plastic deformation becomes smaller. Instead, the elastically deformed or rigid zone starts to occupy more and more cross-sectional area of the chip. The emergence of this elastically deformed region can be thought of as the formation of force amplification through a lever. In other words, the formation of the elastic zone leads to a decrease in the energy required from the tool for chip formation. It is equivalent to an increase in Ich and Ac in Eq. (2.27) and leads to a decrease in the chip plastic deformation. Moreover, it is possible to limit the region of plastic deformation near the cutting edge to certain optimum limits so that the chip-cantilever can transmit the maximum energy from the cutting tool to this region. As such, the contribution of the bending stress in the formation of the combined stress in the chip formation region is the greatest. The formation of the elastically deformed part of the chip begins at a certain cutting speed at which a dramatic change in the energy spent in the plastic deformation should be observed. Then, as the cutting speed increases, the dimensions of the elastic region increase, stabilizing at a certain point because the dimensions of the elastic region cannot exceed those of the layer to be removed. The strain rate can be thought of as a ratio of the deforming velocity and the length of deformation. In cutting, the cutting speed (ν) is the velocity of deformation of the layer being removed. As shown in [2], the strain rate can be represented as a function of this velocity as e˙ =

ν , Ld

(2.29)

where Ld is the length of the deformed specimen in the direction of the cutting speed.

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Tribology of Metal Cutting

On the other hand, by definition, the strain rate is defined as ε˙ =

dε dτ

(2.30)

Combining Eqs. (2.29) and (2.30), one can obtain the following differential equation dε ν = dτ Ld

(2.31)

τct ν = ε + C1 , Ld

(2.32)

which has the following solution

where ε = ln ζ is the true strain, C1 is a constant equal to the value of ln ζ when ν = 0. Finally, the correlation between the CCR and the cutting speed (deformation velocity) can be obtained from Eq. (2.32) as

ζ=e

C1 − Lτν



d

(2.33)

As follows from Eq. (2.33), CCR decreases with the cutting speed according to the exponential curve. The foregoing analysis suggests that the cutting speed influences the energy spent on the deformation of the chip through the temperature, dimensions of the deformation zone adjacent to the cutting edge and the velocity of deformation. The impacts of these factors can be summarized as follows (Fig. 2.6):

Chip compression ratio

• The influence of chip temperature on the work done over the chip in its plastic deformation can be estimated using CCR as follows: increasing the cutting speed

4 1 2 3 Cutting speed

Fig. 2.6. Formation of the resultant dependence of CCR on the cutting speed (after Astakhov [28]).

Energy Partition in the Cutting System

87

leads to an increase in the temperature of the chip so that its plastic deformation increases (curve 1 in Fig. 2.6). • The work done in the plastic deformation of the chip decreases when the deformation velocity increases according to Eq. (2.33). It is represented by curve 2 in Fig. 2.6. • The elastic zone at the tool–chip contact formed at a certain cutting speed leads to the reduction in the plastic deformation of the chip and thus lowers the CCR, starting from this cutting speed. Then, the amount of plastic deformation due to the formation of the elastic zone increases and stabilizes at a certain level as reflected by curve 3 in Fig. 2.6. Summing up the influence of these factors caused by and dependent on the cutting speed, one can obtain the resultant curve 4 (Fig. 2.6), which resembles the known curve of the influence of the cutting speed upon CCR obtained experimentally [12]. The analysis presented, however, allows us to understand the relative impact of different factors correlated with the cutting speed on the plastic deformation of the chip and thus to understand the physics of the phenomenon. The influence of many important external parameters such as the cutting fluid, pre-heating, cryogenic cooling, MQL technique, and many others can be evaluated in terms of their influence on the efficiency of the chip formation process.

2.4.4 Generalization Other parameters that have a strong influence on CCR are the cutting feed (f ), tool cutting edge angle (κr ), cutting edge inclination angle (λs ) and tool rake angle (γn ). As known [7], the cutting feed (f ), tool cutting edge angle (κr ) and cutting edge inclination angle (λs ) affect CCR through the uncut chip thickness (t1 ) which, in turn, may have a different influence at different cutting speeds (ν). This probably was the root cause for many inaccurate conclusions drawn from experimental results in the past. To resolve the problem, the power of the similarity theory in metal cutting should be utilized [2]. The Péclet criterion. The metal cutting system includes moving heat sources, i.e. the tool moves relative to the workpiece and the chip moves relative to the tool. As a result, similarity numbers used in thermodynamics to deal with moving heat sources [23–25] should be utilized for thermodynamic analyses of metal cutting. Unfortunately, this is not the case in traditional studies on thermal aspects of metal cutting including tribological interfaces where traditional steady-state thermodynamic analysis of heat transfer commonly used today as, for example, in [20,26,27]. The Péclet criterion, often referred to as the Péclet number, is widely used in the thermal analysis of technical systems subjected to moving heat sources [23–25]. As pointed out by Astakhov, this criterion should be used in metal cutting [2]. The Péclet criterion is a dimensionless number expressing the ratio of advection to thermal diffusion. It is expressed by Pe =

UL , ww

(2.34)

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Tribology of Metal Cutting

where U is the velocity scale, L is the horizontal length scale and ww is the thermal diffusivity. Molecular diffusion of heat is negligible when Pe > 10, i.e. a heat source moves faster than the velocity of heat expansion. In metal cutting, the Péclet criterion is represented in terms of machining process parameters as follows [2,28] Pe =

νt1 , ww

(2.35)

where ν is the velocity of a moving heat source (the cutting speed) (m/s) and ww is the thermal diffusivity of the work material (m2 /s), ww =

kw , (cp ρ)w

(2.36)

◦ where kw is the thermoconductivity ofwork  (J/(m · s · C)) and (cp ρ)w is the  3material ◦ volume specific heat of work material J/ m · C .

The Péclet number is a similarity number, which characterizes the relative influence of the cutting regime (νt1 ) with respect to the thermal properties of the workpiece material (ww ). If Pe > 10, the heat source (the cutting tool) moves over the workpiece faster than the velocity of thermal wave propagation in the work material and so, that the relative influence of the thermal energy generated in cutting, on the plastic deformation of the work material is only due to the residual heat from the previous tool position [8]. If 2 < Pe < 10, the thermal energy makes its strong contribution to the process of plastic deformation during the cutting and thus to the tribological conditions at tribological interfaces. Calculations of Pe for different cutting conditions can be found in [2]. In metal cutting tests, a simplified form of the Péclet criterion (νt1 ) can be used for a given work material. Experimental results. Figure 2.7(a) shows the influence of cutting speed on CCR for different feeds. Figure 2.7(b) shows what happens if the Péclet criterion is used as the independent variable. Figure 2.8 presents another example of the experimental data obtained in the machining of tool steel H13. Such a representation allows the reduction in the number of cutting tests needed to study the amount of plastic deformation in the metal cutting process. Moreover, it helps in revealing the mutual influence of the cutting regime, tool geometry and physical properties of the work material on this plastic deformation. For example, it is clearly shown that the amount of plastic deformation in cutting a work material having low thermoconductivity is greater, compared to that in cutting a work material having higher thermoconductivity, if the other cutting parameters remain the same. It can be stated that the experimental results obtained, for the first time, reveal the correlation of the thermoconductivity of the work material and the amount of plastic deformation in its machining. In other words, the results obtained quantify one of the most important qualitative characteristics of the work material,

Energy Partition in the Cutting System

89

z 0.125 mm/rev

2.4

(a)

0.200 mm/rev

2.2

0.280 mm/rev 0.390 mm/rev

2.0

0.500 mm/rev 0.75 mm/rev

1.8 0

1.0

2.0

3.0

0

70

140

280

n (m/s)

z 2.4

(b)

2.2

2.0

1.8

Pe

Fig. 2.7. The chip compression ratio vs. cutting speed for different feeds (a) and generalized correlation between CCR and Pe criterion (b). Work material – steel AISI 1030, tool material – carbide P20, rake angle γn = 10◦ , cutting edge angle κ1 = 60◦ , depth of cut dw = 2 mm (after Astakhov [28]).

i.e. “machinability.” Using the work of plastic deformation which is the sole property of the work material involved in the cutting process, one can determine machinabilities of various work materials quantitatively. Analyzing the results discussed, one may argue that the influence of tool geometry is not accounted for. To address this concern, the following should be explained. The tool rake angle is the only tool geometry parameter that might affect the work of plastic deformation. The influence of the tool rake angle on CCR is shown in Fig. 2.9. As shown, CCR does not depend on the tool rake angle. Based upon the results obtained, the following generalizations can be made: • Plastic deformation is a nuisance for the metal cutting process and thus it should be reduced in order to increase the efficiency of the process. The rule of thumb here is: less the plastic deformation, better the cutting process. • The final shear strain used to assess plastic deformation in metal cutting is not a relevant characteristic because it does not correlate with the known properties of

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Tribology of Metal Cutting

z f = 0.1 mm/rev

(a)

3.0 0.2 mm/rev 0.3 mm/rev 2.0 0

1

2

n(m/s)

0

70

140

Pe

z

3.0

(b) 2.0

Fig. 2.8. CCR vs. Pe criterion. Work material – tool steel H13, tool material – carbide M10, rake angle γn = −10◦ , cutting edge angle κr = 60◦ , depth of cut dw = 2 mm (after Astakhov [28]).

z g:

+20° +10° 0° −10° −20°

2.8

2.0

1.2 70

140

210

Pe

Fig. 2.9. CCR vs. Pe criterion for different rake angles. Work material – steel AISI 1045, tool material – carbide P20, cutting edge angle κr = 60◦ , depth of cut dw = 2 mm (after Astakhov [28]).

the work material. CCR represents the true strain in plastic deformation and can be used to calculate the elementary work spent over plastic deformation of a unit volume of the work material. Knowing the elementary work, the total work done by the external force applied to the tool can then be calculated. As a result, CCR can be used as the prime parameter for the optimization of the metal cutting process. Considered together with the work of plastic deformation, CCR reveals the energy spent in cutting. Moreover, CCR is a post-process parameter and thus there are a number of simple, though forgotten, ways to measure this parameter accurately in metal cutting.

Energy Partition in the Cutting System

91

• The cutting speed influences the energy spent on the deformation of the chip through the temperature, dimensions of the deformation zone adjacent to the cutting edge and the velocity of deformation. For the first time, the relative impact of each of these parameters on the chip compression ratio is revealed, and thus the experimental dependence of CCR on the cutting speed is explained. • To avoid the typical misrepresentation of the experimental data on CCR, it is proposed to determine this parameter as a function of the Péclet criterion. Such a representation allows accounting for the combined influence of the cutting regime and physical properties of the work material.

2.5 Practical Analysis of the Physical Efficiency of the Cutting System A series of turning tests were carried out to reveal the influence of various parameters of the cutting system on its efficiency. General purpose cutting inserts made of P20 carbide, having the shape SNMM 150612 SN-HT were selected for the test. A special tool holder was designed and made to provide these inserts with various rake angles. Figure 2.10 shows the influence of rake angle. As shown, the efficiency of the cutting system increases with the rake angle, this result was anticipated because it follows the usual machining practice. More pronounced effect of the rake angle is observed when the depth of cut, cutting speed and feed are increased. This influence is greater for difficult-to-machine materials (as an example, the results for steel AISI 52100 are presented). Figure 2.11 shows the influence of depth of cut. As shown, the depth of cut may affect the efficiency of the cutting system in considerably different ways depending upon the particular combination of the cutting parameters and properties of the work material. The results obtained are in contradiction to the common belief that the cutting process becomes “better” as the depth of cut increases. Figure 2.12(a) shows the influence of cutting speed on the efficiency of the cutting system. As shown, although this influence depends on many cutting parameters, the influence of work material is of prime importance. This is natural because a great part of the energy “wasted” in the cutting process is spent on the plastic deformation of the chip and the workpiece surface. Therefore, machining of more brittle work materials is more efficient than that of the ductile ones. Although this fact is well known in machining practice, the existing metal cutting theory, operating with shear strength and flow-shear stress, cannot explain it. However, when one accepts the approach discussed, this problem disappears (as well as many other problems in understanding and implementation of the metal cutting theory). Although the influence of cutting speed according to Fig. 2.12(a) seems to be at odds with the existing perception of machining, it is correct because increasing the cutting speed causes higher heat generation on the tool–chip and tool– workpiece interfaces. Moreover, because CCR decreases with the cutting speed (Fig. 2.9), the relative tool–chip velocity increases even further causing the intensification of heat generation at the tool–chip interface and thus additional energy losses. The cutting feed has a marked effect on the system efficiency (Fig. 2.12(b)) for difficultto-machine and brittle materials, while the influence of cutting speed and depth of cut

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Tribology of Metal Cutting

Steel 52100, n = 0.5 m/s, dw = 1 mm

Steel 52100, f = 0.11 mm/rev, dw = 1 mm

60

60

n = 0.3 m/s

Efficiency, ηcs(%)

f = 0.17 mm/rev 50

50 n = 0.5 m/s

40

f = 0.11 mm/rev

40 n = 0.6 m/s

30

−10

30

f = 0.07 mm/rev

+10

0 Rake angle, g (°)

−10

0 Rake angle, g (°)

+10

Steel 52100, n = 0.5 m/s, f = 0.11 mm/rev

60

dw = 1.0 mm 50

40

dw = 0.5 mm

dw = 1.5 mm 30

−10

0 Rake angle, g(°)

+10

Fig. 2.10. Influence of rake angle on the efficiency of the cutting system. Work material – steel AISI 52100 (after Astakhov [3]).

80 n = 0.5 m/s, s = 0.11 mm/rev Efficiency of the cutting system, ηcs(%)

3 2

20

1

1 − g = −10° 2 − g = 0° 3 − g = +10°

AISI 52100

0.5 80

1.5

n = 1.2 m/s, s = 0.11 mm/rev 3 2

1 AISI 1045

20 0.5

1.5

Depth of cut, dw (mm)

Fig. 2.11. Influence of depth of cut on the efficiency of the cutting system for different work materials (after Astakhov [3]).

(a)

(b) f=0.11 mm/rev, dw =1 mm 3

1 − g = −10° 2 − g = 0° 3 − g = +10°

n =0.5m/s, dw =1 mm

3

2

2 1

Efficiency of the cutting system,hcs(%)

1 AISI 52100

20 h

0.6

80 2

AISI 52100

20

0.3

f=0.11 mm/rev, dw =1 mm

1 − g = −10° 2 − g = 0° 3 − g = +10°

0.07 80

0.17

f=0.11 mm/rev, dw =1 mm 2

3

3 1 1 AISI 1045

20 0.8 80

AISI 1045

20 0.07

1.5 80

g = 0°

0.17

g = 0° Gray cast iron, n =3m/s, dw =1 mm

Gray cast iron, n =3m/s, dw =1 mm Steel AISI1035, n =1.5m/s, dw =1 mm

Steel AISI1035, n =1.5m/s, dw =1 mm 20

20 0

Cutting speed, n (m/s)

5

0.07

Cutting feed, f (mm/rev)

0.17

Fig. 2.12. Dependence of the efficiency of the cutting system on: (a) cutting speed and (b) cutting feed (after Astakhov [3]).

94

Tribology of Metal Cutting

are more noticeable for easy-to-machine materials. These results also reflect the wellknown practical finding that one should use as high feed as allowed by the strength of the tool, quality of machining and other constraints in order to increase the efficiency of the cutting system. It follows from the data presented in Figs. 2.10–2.12 that the efficiency of the cutting system depends to a large extent on the properties of the work material. For a wide range of commonly machined steels, this efficiency is in the range of 25–60%. It means that 40–75% of the energy consumed by the cutting system is simply wasted. Most of this wasted energy is spent at the tool–chip and tool–workpiece interfaces. Naturally, this energy lowers the tool life, affects the shape of the chip produced, and leads to the necessity of using different cooling media that, in turn, lowers the efficiency of the machining system as more energy is required for the cooling medium delivery and maintenance. The results obtained are of enormous significance in metal cutting as they primarily quantify the margin allowed for process improvements. Even in machinery, where the waste of resources (energy) due to the ignorance of tribology hardly exceeds single digit, this waste is estimated to be approximately one-third of the world’s energy consumption [1]; so the study and optimization of tribological process are considered as having great importance. Today, more money is spent for the research in tribology. The objective of this research is understandably the minimization and elimination of losses resulting from friction and wear at all levels of technology where rubbing of surfaces is involved. As claimed [1], research in tribology leads to greater plant efficiency, better performance, fewer breakdowns and significant savings. In metal cutting, the situation is entirely different from that of the design of tribological joints in modern machinery. In the latter, a designer is rather limited by the shape of the contacting surfaces, materials used, working conditions set by the outside operating requirements, use of cooling and lubricating media, etc. In metal cutting, practically any parameters of the cutting system can be varied in a wide range. The modern machine tools do not limit a process designer with the selection of cutting speeds, feeds and depth of cut. The tool materials, geometry of cutting inserts and tool-holder nomenclature available at his disposal is very wide. The selection of cooling and lubrication media and their application techniques are practically unlimited. Although the chemical composition of the work material is normally given as set by the part designer, the properties of this material can be altered in a wide range by heat treatment, forging and casting conditions. The only problem in the selection of the optimal tribological cutting parameters is the lack of knowledge on the metal cutting tribology. Therefore, the study and optimization of the tribological conditions at these interfaces have a great potential in terms of reduction in the energy spent in cutting, increase in tool life, reduction and elimination of coolants, etc.

2.6 Energy Balance of the Cutting System To improve the analysis and optimization of the cutting system, one should first analyze the energy flows in it, besides determining its efficiency. Because any alteration of the system parameters leads to a change in the energy distribution within the cutting system.

Energy Partition in the Cutting System

95

Although the distribution obtained may not affect the physical efficiency of the cutting system, it might change the outcomes of the cutting process. For example, the use of coating applied on the tool contact surfaces may improve the tool life. At the same time, it changes the distribution of thermal energy in the cutting system. Because many coating, particularly multi-layered, have low thermal conductivity, and a greater portion of the thermal energy generated in the cutting process goes into the workpiece creating higher machining residual stresses compared to uncoated tools. This is a typical example of the non-system consideration of the cutting process to improve a single outcome while others may get much worse. Therefore, a special master program should be developed not only to calculate the efficiency of the cutting system, but also to analyze the energy flows in this system. In the author’s opinion, such a program should use a flowchart of energy flows in the cutting system similar to that shown in Fig. 2.13. Using this flowchart, the correlation between these energy flows and the properties of the cutting system can be established in order to evaluate the efficiency of this cutting system. Energy losses due to friction and deformation of the cutting wedge (Q1 ) and the chip (Q6 ) are unavoidable. As such, the energy loss in the cutting wedge can be thought of as

Q1 = f1 AT1 , EpT , υpT , σpT ,

(2.37)

where f1 is the known function explained in [29–32], AT1 is the potential energy of the cutting wedge and EpT , υpT and σpT are the in-process mechanical characteristics of the cutting wedge material (tool material) (the modulus of elasticity, Poisson’s ratio, strength). These energies depend on the original mechanical characteristics of the cutting wedge material and the thermal energies accumulate in the cutting wedge   EpT = f2 ET , Qtγ , Qtα , QT1 , QeT   υpT = f3 υT , Qtγ , Qtα , QT1 , QeT   σpT = f4 σ T , Qtγ , Qtα , QT1 , QeT ,

Wtg

Q3

QeT Ucs

Q2

(2.40)

Uw

Uc

Wta

(2.39)

Q5

Qec

UT Q1

(2.38)

Q6

Wf Qew

Uf Q4 Qw

Fig. 2.13. Flowchart of energy flows in the cutting system.

96

Tribology of Metal Cutting

where f2 , f3 and f4 are the functions described in [33], ET , υT and σ T are the standard mechanical characteristics of the cutting wedge material (tool material), QT1 is a part of Q1 accumulated in the tool and Qtγ , Qtα and Q1 are the thermal energies shown schematically in Fig. 2.13. Qtγ = f5 (Q2 , kT , kw , VT , Vw , lc , dwc )   Qtα = f6 Q3 , kT , kc , VT , Vc , Acf

(2.41)

QT1 = f7 (Q1 , kT )   QeT = f8 Qtγ , Qtα , QT1 ,

(2.43)

(2.42)

(2.44)

where f5 –f8 are the functions described in [30,31,34–38], kT , kw and kc are the thermoconductivities of the tool material, workpiece material and material of the chip, respectively, VT , Vw and Vc are the volumes of the tool, workpiece and chip, respectively, lc and dwc are the tool–chip contact length and width, and Acf is the flank contact area. The heat generated due to friction on the tool rake face is calculated as   Q2 = f9 Wtγ

(2.45)

and the heat generated due to friction on the tool flank surface is Q3 = f10 (Wtα )

(2.46)

Functions f9 and f10 are described in [2,12,27,30,31]. The potential energy of the tool, UT = Ucs − Q1

(2.47)

is spent on the friction work done on the rake and flank surfaces   Wtγ = f11 UT , υT , lc, dwc   Wtα = f12 UT , υT , Acf

(2.48) (2.49)

and on the work done over the chip. The energy loss in chip deformation is calculated as

Q6 = f13 UTc , Epc , υpc , σpc ,

(2.50)

where f11 –f13 are the functions described in [11,12,27,30], UTc = UT − Wtγ − Wtα is a part of WT which is spent on the work done over the chip, and Epc , υpc and σpc are the

Energy Partition in the Cutting System

97

in-process mechanical characteristics of the material of the chip.   Epc = f14 Ec , Qtc , Qfc , Qc6   υpc = f15 υc , Qtc , Qfc , Qc6   σpc = f16 σ c , Qtc , Qfc , Qc6 ,

(2.51) (2.52) (2.53)

where f14 –f16 are the functions described in [39], Ec , υc and σ c are the mechanical characteristics of the material of the chip and Qc6 is a part of Q6 accumulated in the chip, andQtc , Qfc and Q6 are thermal energies shown in Fig. 2.1. Qtc = f17 (Q2 , kT , kc , VT , Vc , lc , dwc )

(2.54)

Qfc = f18 (Q4 , kc , Vc , νch )

(2.55)

= f19 (Q6 , kc , Vc , νch ) ,

(2.56)

Qc6

where f17 –f19 are the functions described in [31,32,36,37,40–42], νch is the velocity of the chip which appears to be the velocity of heat transmission, νch = νζ, and Q4 is the thermal energy generated   due to the deformation and fracture of the chip in the chip forming zone, Q4 = f20 Uf [43,44]. The potential energy of the chip is calculated as Uc = UTc − Q6

(2.57)

This energy makes contribution Wf to the formation of the fracture energy U1 , which includes the work done in the formation of new surfaces [43] and to the work spent on the deformation of the surface layer of the workpiece Uw . As such, a part of the heat generated is conducted into the workpiece Qfw = f21 (Q4 , Vw , kw )

(2.58)

Qtw part of the heat generated at the tool flank contact surface Q2 is also conducted into the workpiece Qtw = f22 (Q2 , Vw , kw )

(2.59)

Besides, Qw 5 part of the heat Q5 generated due to the plastic deformation of the surface layer of the workpiece is also accumulated in the workpiece Qw 5 = f23 (Q5 , Vw , kw ) ,

(2.60)



Q5 = f24 Wdw , Epw , υpw , σpw ,

(2.61)

where

98

Tribology of Metal Cutting

where Epw , υpw and σpw are the in-process mechanical characteristics of the work material and Wdw is the work spent on the deformation of the surface layer of the workpiece, Wdw = f25 (Uc , ρce , α, γ, ν) ,

(2.62)

where ρce is the cutting edge radius and α, γ are the flank and the rake angles, respectively. Functions f21 –f24 are described in [2,12,31,32,34,35,37,39–42,44–47]. The overall thermal energy that flows into the workpiece is then calculated as Qw = Qtw + Qfw + Qw 5

(2.63)

The energy of fracture and separation of the layer being removed is practically constant for a given cutting system. It forms as consisting of the following terms due to the discussed organization of the cutting system Uf = Wf + Qwf + Qfr ,

(2.64)

where Qwf is a part of the heat generated due to deformation of the workpiece, Qfr is the residual heat transferred from the previous position of the cutting tool [48],   (2.65) Qfr = f26 Q5 , nw , dwp , νf , νk , where nw is the rotational speed of the workpiece (rpm), dwp is the workpiece diameter, νf is the feed velocity or feed rate, νf = nw f and νk is the velocity of heat conduction. When the diameter of the workpiece is small, the thermal energy Qwf = f27 (Qw , Vw ) can become noteworthy and thus, according to Eq. (2.64), its contribution to the formation of the fracture energy becomes significant. The cutting system now requires less energy since Wf decreases during the process. The set of equations (Eqs. (2.37)–(2.65)) represents the energy balance of the cutting system showing correlations among its components. A stable state of the cutting system and thus the ratios of the energy flows are determined according to the system thermodynamic equilibrium [2], which follows the principle of minimum energy. 2.7 Methods of Improving Physical Efficiency of the Cutting System Efficiency of the cutting system can be increased not only by reducing the difference between the energy needed for the separation of the layer being removed and that required by the cutting system, but also primarily by decreasing the energy required for the separation of the layer being removed. This goal can be achieved principally in two different ways: The first one can be referred to as the external method where the means are supplied from outside the cutting system (for example, application of the cutting fluid, preheating of the workpiece, etc.). This is discussed in Chapter 6.

Energy Partition in the Cutting System

99

The second method is internal, where the same effect is achieved by certain arrangement of the components of the cutting system. In the author’s opinion, the second method is the simplest and the most efficient. Two novel methods of its practical realization are discussed in the next section.

2.7.1 Method 1: using interactions of energy waves Internal energy of the layer being removed. A part of the mechanical energy spent on the plastic deformation of the layer being removed, as well as the energy spent on friction and plastic deformation on the rake and flank faces, convert into heat. This thermal energy should also be considered in the analysis of the cutting system. According to the energy theory of failure, a given volume of the work material fails when the critical internal energy is accumulated in this volume. This critical internal energy can be of any kind or the sum of different input energies [6]. This postulate, referred to as the internal energy principle, is used in this work. According to the internal energy principle, the internal energy of the cutting system has to be considered and particular attention is to be paid to the energy accumulated in the layer being removed just in front of the cutting edge. As such, an infinitesimal increment of the internal energy (dWin ) of this layer can be represented as the sum of the mechanical energy supplied from outside (dA) and thermal energy realized in the system dQ, i.e. dWin = dA + dQ

(2.66)

Interaction between deformation and thermal waves in the machining zone. Internal energy principle. According to the second law of thermodynamics [49], thermal energy does not flow from regions having lower temperatures to those having higher temperatures. Because the machining zone (a small zone around the cutting edge where the elastic and plastic deformations of the layer being removed take place) is a heat source, its temperature is always higher than that of the rest of the work material. As a result, the thermal energy should flow from this zone so that it seems that the “−” sign should be assigned to the second term of Eq. (2.66). However, it will be demonstrated that the “+” sign before the term dQ in Eq. (2.66) can be justified in the metal cutting system. Because the machining zone moves with a certain velocity with respect to the workpiece, the thermal energy from the deformation zone can enter into the layer being removed ahead of this zone if and only if the velocity of heat transfer exceeds the velocity with which the machining zone moves over the workpiece. The thermal energy realized at a given instant in the machining zone forms a certain dynamic energy field in the workpiece around this zone at the instant considered. As such, there is no particular direction of heat transfer, i.e. heat transfers in all directions at the same rate in homogeneous media. A region on the workpiece over which the cutting system moves at the time instant considered, is therefore a decaying heat source. Heat transfers from this source, and so an increment of heat energy dQ, is the residual heat transferred in the location of the

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cutting system considered from its previous position, provided that heat transfers faster than the cutting system moving from the previous to the current position. The relative velocity of a moving heat source is characterized by the Péclet number (Eq. (2.35)). As discussed above, if Pe > 10, the heat source (the cutting tool) moves over the workpiece faster than the velocity of thermal wave propagation in the work material so that the relative influence of the thermal energy generated in cutting on the plastic deformation of the work material is only due to the residual heat from the previous tool position [8]. This is the case for the values of terms of Eq. (2.66) used in the practice of metal cutting. The calculations known show that in many cases, the velocity of the cutting system exceeds that of heat transfer in the same direction [2]. However, this is true only for the pure orthogonal cutting, where the tool never passes the same, or even the neighboring point of the workpiece more than once (Fig. A1.1(a)). In practical machining operations (turning, milling, drilling, etc.), the feed is used to generate the machined surface. As such, the cutting tool advances into the workpiece with the feed velocity, which is considerably smaller than the cutting velocity so that the residual heat from the previous pass might significantly affect the cutting process on the current pass. The smaller the time interval between the two successive tool positions (i.e. with smaller workpiece diameter and higher cutting speed), the greater the effect of the residual heat. As such, the “+” sign of the term dQ in Eq. (2.66) does not contradict the second law of thermodynamics, i.e. first the heat moves into a region having lower temperature and then the cutting system moves into the same region. The current discussion suggests that the feed velocity νf (in turning, it is calculated as νf = fn (m/s), where f is the feed per revolution (m/rev) and n is the rpm of the workpiece (tool)) should be compared with the velocity of heat conduction νq . Such a comparison suggests that if νf = νq , the maximum heat energy enters the cutting system and thus the residual heat has the strongest influence on the cutting process [8]. According to the internal energy principle, the energy of failure (fracture) of the layer to be removed is constant under the given machining conditions. Thus, according to Eq. (2.66), less mechanical energy (dA) is needed for the fracture of the layer being removed, when more heat energy (dQ) is available in the current position of the cutting system. Coherent energy waves. It was discussed in Chapter 1 that the chip formation process is cyclic, and thus the cutting force and the thermal energy generated in metal cutting change within each cycle of chip formation. The frequency of chip formation was proved to depend on the cutting speed and on the properties of the work material. Therefore, this process generates the deformation and thermal waves. Because these two are generated by the same source, namely, the chip formation process (or simply, the tool), these waves must be coherent. To comprehend the concept of interaction of coherent energy waves, simple turning is considered as an example. In turning, the internal energy in the layer being removed increases according to Eq. (2.66) due to heat conduction in the feed direction. As the workpiece completes one revolution, the thermal energy, generated at the previous position of the cutting system, reaches the current position of this system. Calculations

Energy Partition in the Cutting System

101

y

t1 t3

t2

x

Fig. 2.14. Intensity of a decaying heat source.

show [2] that the cutting speed significantly exceeds the velocity of heat conduction, while the feed rate (feed velocity) commensurates with this velocity. Since the intensity of a decaying heat source obeys the normal law, the distribution curve transforms into an almost straight line with time τ, as shown in Fig. 2.14, where the instants of consideration are as follows: τ1 < τ2 < τ3 . Physically, it means that a certain nearly constant temperature field is established within the volume considered over time. If the feed rate (νf ) is equal to the velocity of heat conduction (νq ), the maximum heat energy is supplied into the cutting system. However, if νf > νq dQ = 0 and, if νf < νq , then the heat energy supplied to the cutting system is less than the maximum (Fig. 2.14). According to the internal energy principle, the energy of failure (fracture) of the layer being removed is constant under the given machining conditions [6]. The time interval between the two successive tool positions (between the neighboring trajectories of the cutting tool) depends on the cutting speed ν, and the diameter of the workpiece Dw and is calculated as τ2 =

πDw ν

(2.67)

Table 2.2 shows the results of the calculations of the time intervals for two different diameters of the workpiece. If the cutting tests are conducted under the conditions indicated

Table 2.2. Feed velocities and time difference between two successive positions of the cutting tool. ν (m/s) 1 5

Dw = 80 mm −3 νf × 10 (m/s) τ2 (s) 0.28 1.39

0.25 0.05

Dw = 100 mm νf × 10−3 (m/s)

τ2 (s)

0.22 1.11

0.31 0.063

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in Table 2.2, each combination of parameters should result in different consumption of mechanical energy. This fact can be verified by using the measurements of the cutting force because this mechanical energy is calculated as A = Fz ντ2

(2.68)

According to Truesdell and Noll [50], a wave is considered as the means by which a given system moves from one state to another with a finite velocity. It is also known that energy moves in waves [51]. Thermal waves formed at the preceding position of the cutting system move in the workpiece in the feed direction with a certain velocity, which depends only on the properties of the work material (its thermal diffusivity) and hence this velocity is constant for a given work material. Reaching the current position of the cutting system, these waves interact with those due to deformation. Since the thermal energy in the system is a part of the mechanical energy transformed, their frequencies should be the same. Different feeds should result in phase differences between the mechanical and thermal waves. As a result, maximum reinforcement (or constructive interference) of the mechanical and thermal waves takes place when they have the same phase, while maximum destructive interference takes place when their phases are opposite. It is clear that a number of intermediate states are possible depending on a particular phase difference. The phase difference exists between the two neighboring trajectories (threads) of the moving cutting edge. As such, a decaying heat source generates thermal waves at the previous trajectory, while the cutting edge at the current trajectory generates a deformation wave. The distance between the neighboring trajectories (feed per revolution) is the path difference of the waves considered. As indicated in [8], the interaction of such longitudinal waves results in the reinforcement of energy (constructive interference) when these waves are in-phase, i.e. when the path difference, represented by the feed, is f =

1 2kl0 , 2

k = 0, 1, 2, . . .

(2.69)

where l0 is the wavelength. On the contrary, when the path difference is f =

1 (2k + 1) l0 , 2

k = 0, 1, 2, . . .

(2.70)

these waves have opposite phase which results in their destructive interference. The physical picture discussed is illustrated in Fig. 2.15, where external bar turning and the corresponding cutting tool trajectory are shown. Let us consider a microvolume of the work material located at Point 2 on the tool trajectory (Fig. 2.15(b)) at the instant when the tool passes this point. According to Eq. (2.66), a change in the internal energy (dWin ) of the microvolume is the sum of the mechanical work done by the external forces (dA) applied by the tool and the residual thermal energy (dQ) entering the current position

Energy Partition in the Cutting System

103

f

Win

x

Q

A

2

v

1

Workpiece

Tool

f

(a)

(b)

Fig. 2.15. (a) External bar turning and (b) the trajectory of the cutting tool (after Astakhov [8]).

from the identical volume located on the neighboring trajectory of the tool (from Point 1, Fig. 2.15(b)). As shown, the residual heat dQ in Eq. (2.66) is positive because this heat is transferred into the microvolume at Point 2 (when the cutting tool reaches there) from the decaying heat source of Point 1 (the preceding position of the cutting tool), if and only if the velocity of heat conduction in the workpiece is equal to or greater than the translation speed of the cutting system along the feed direction (the x direction in Fig. 2.15(b)). Consider a typical example: workpiece material: AISI steel 1045 having thermal diffusivity ww = 6.75 × 10−6 m2 /s, cutting speed ν = 180 m/min, cutting feed f = 0.15 mm/rev, workpiece diameter Dw = 100 mm, tool cutting edge angle κr = 60◦ . As such, the uncut chip thickness t1 = f sin κr = 0.15 sin 60◦ = 0.13 mm and the feed velocity (which is the velocity of the heat source) νf = nw f = 103 ν/πdwp × f = 103 × 180 × 0.15 × 10−3 /3.141 × 100 = 0.086 m/min or νf = 0.00143 m/s. Substituting νf , t1 and ww into Eq. (2.35), one can calculate Pe = 0.0275. As Pe < 10, there is no contradiction with the laws of thermodynamics in Eq. (2.66) – first heat enters the less heated zone (Point 2, Fig. 2.15(b)) and then the cutting tool (as a heat source) moves there, thus the residual heat in Eq. (2.66) is positive. Experimental verification. The experimental verification of the internal energy principle formulated and interactions of the coherent waves discussed was carried out using a turning test. Hot rolled bar stock of steel AISI 4140 was used as the workpiece. The actual (as tested upon receiving) chemical composition was: 0.39% C, 0.72% Mn, 0.012% P, 0.001% S, 0.31% Si, 1.03% Cr and 0.16% Mo. The hardness of the work material was 221 HB. A retrofitted Schaerer HPD 631 lathe was used as the test machine. A two-component Kistler Type 9271A dynamometer was used. Based on the standard mounting as specified by the supplier (Kistler), the load washer (Kistler Type 9065) was installed in the dynamometer and pre-loaded to 120 kN. At this pre-load, the range

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for force measurements is from −20 to +20 kN; threshold is 0.02 N; sensitivity is −1.8 pC/N; non-linearity does not exceed a value of ± 1.0% FSO; overload is 144 kN; crosstalk does not exceed 0.02 N/N; resonant frequency is 40 kHz; temperature error does not exceed +30 N/◦ C. The load washer was connected to the dual-mode charge amplifiers (Kistler, Mod. 5010B). The static and dynamic calibrations were performed according to the methodology presented in Ref. [8]. Four general purpose triangular cutting inserts (ANSI designation TCMT-110204) made of P20 carbide from four different carbide suppliers were selected for the test to avoid bias due to particular carbide properties. These are numbered 1, 2, 3 and 4. Influence of cutting speed. The test results with insert No. 1 are shown in Table 2.3. Following the conventional way suggested in earlier studies [2,12,13,52], correlations between the cutting speed and cutting force were expressed by the simple power curve relation Fz = Cvx ,

(2.71)

where C and x are constants. Using the experimental results obtained (Table 2.3), the following relationships were obtained: Fz = 53.94 ν−0.1

when

dw = 0.1 mm

(2.72)

Fz = 193.13 ν−0.1

when

dw = 0.5 mm

(2.73)

−0.1

when

dw = 1.0 mm

(2.74)

Fz = 427.79 ν

The current consideration, however, suggests another type of representation of the experimental results. The experimental points from Table 2.3 were placed in the orthogonal

Table 2.3. Experimental results (insert No. 1). Cutting speed ν (m/s) 0.07 0.11 0.23 0.29 0.46 0.58 0.72 0.92 1.15 1.82 2.30 2.63 4.60 5.76

Cutting force Fz (N) dw = 0.1 mm

dw = 0.5 mm

dw = 1 mm

84 75 47 38 38 56 47 41 47 56 56 60 38 53

328 244 206 206 169 169 178 178 169 187 187 178 169 187

506 469 469 375 375 394 469 450 469 431 469 431 375 366

Energy Partition in the Cutting System

105

470

450

430

Cutting force, Pz (N)

dw = 1.0 mm 410

390

370 190 dw= 0.5 mm 170 60 dw = 0.1 mm 40 1

2

3

4

5

Cutting speed, n (m/s)

Fig. 2.16. Experimental results represented as sinusoidal periodic data in the coordinate system “ν − Pz ” (after Astakhov [8]).

coordinate system “ν − Pz .” With regard to the aforementioned wave nature of deformation, these points were considered as sinusoidal periodic data (Fig. 2.16) that can be represented mathematically as 

  2π  Fz = Fz0 + Fza sin ν + νph , lν

(2.75)

where Fz0 is the mean of the sine wave, Fza , lν and νph are its amplitude, wavelength and initial phase, respectively. The proposed representation of the data of Table 2.3 results in the following models  2π (0.050 + ν) , Fz = 47 + 10 0.56 

when

dw = 0.1 mm

(2.76)

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Tribology of Metal Cutting 

 2π (0.049 + ν) , when dw = 0.5 mm 0.50   2π (0.045 + ν) , when dw = 1.0 mm Fz = 422 + 50 0.46

Fz = 178 + 11

(2.77) (2.78)

The experimental results have also shown that the wavelength of the sine wave lν decreases with the depth of cut. Particularly, when the depth of cut dw = 0.1 mm, the wavelength of the corresponding sine wave approximates the experimental results lν = 0.56 m/s and when dw = 1.0 mm, this wavelength becomes lν = 0.46 m/s. Table 2.4 shows the results of tests conducted under the same conditions with insert No. 2. The comparison of these results (solid lines) with those obtained using insert No.1 (dashed lines) is shown in Fig. 2.17. As shown, the wavelength and the amplitude remain the same while the position of the mean line and the initial phase are shifted. The experimental data obtained allow us to conclude that, under the given cutting regime and tool geometry, the wavelength and the amplitude of the sine wave are determined by the properties of the work material, while the amplitude and the initial phase are determined by the processes taking place at the tool contact surfaces. The latter is evident because the use of insert No. 2 instead of insert No. 1, changed only the contact processes on the tool rake and flank faces due to the difference in the chemical composition of insert materials, surface condition and finish etc., while the other parameters of the cutting system remained the same. Figures 2.16 and 2.17 suggest that the cutting force changes sinusoidally with the cutting speed when other cutting conditions remain the same. This suggestion was verified as follows. A particular sine-wave shape was established under these conditions – cutting feed f = 0.12 mm/rev and depth of cut dw = 0.5 mm (Tables 2.3 and 2.4) – as 

   2π 2π ν = 11 sin ν Fz = Fza sin lν 0.5

(2.79)

Then, cutting tests were carried out with insert No. 3 and insert No. 4 using the same cutting conditions. The corresponding experimental points were placed in the coordinate system “ν − Pz ” and the initial phase of the sine curve described by Eq. (2.79) was

Table 2.4. Experimental results (insert No.2). Cutting speed ν(m/s) 2.80 3.03 3.30 4.18 4.27 4.45 5.25 5.33

Cutting force Fz (N) dw = 0.1mm

dw = 0.5mm

dw = 1mm

66 66 38 75 51 75 79 71

187 225 221 206 206 216 234 216

394 394 403 394 394 375 403 394

Energy Partition in the Cutting System

107

470 dw= 1.0 mm

Cutting force, Pz (N)

370

190

dw = 0.5 mm

170

60

dw = 0.1 mm

40 1

2

3

4

5

Cutting speed, n (m/s)

Fig. 2.17. Scatter for cutting inserts No. 1 and No. 2.

determined. Figure 2.18 shows that the experimental points fit this curve fairly good, accounting for the accuracy with which the cutting force can be measured. The experimental results show that the cutting force changes sinusoidally with the cutting speed. If the tool geometry and location of the cutting tool with respect to the workpiece surface are kept constant, the energy of failure (fracture) of the layer to be removed remains constant too. Therefore, according to Eq. (2.66), the mechanical energy required should be a function of the cutting speed. If the interaction of deformation and thermal waves causes their reinforcement then the required mechanical energy decreases. On the contrary, if this interaction results in destructive interference, the required mechanical energy increases. When the cutting feed is constant, the path difference of the coherent waves does not change. According to Eq. (2.66), a change in the cutting speed results in the change in the time interval between the two successive tool positions (between the neighboring trajectories of the cutting tool), which is, according to Eq. (2.66), equivalent to a change in the intensity of the heat source. Therefore, it becomes clear that the revealed dependence of the interaction of the energy waves on the cutting speed is possible only if the frequency of deformation and heat waves depends on this speed. The phenomenon of interaction of the deformation and thermal longitudinal waves was additionally examined using the following logic: the interaction of the waves takes place

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Tribology of Metal Cutting

Cutting force, Pz (N)

250

220

190

160 1

2

3

4

5

8

Cutting speed, n (m/s)

Fig. 2.18. Experimental results for cutting inserts No. 3 and No. 4.

due to the fact that these waves are coherent. Therefore, if the coherence of the waves is disturbed, the interaction should not be observed. To verify this statement, the second series of experiment was carried out using face cutting (Fig. 2.19a). Table 2.5 lists the ranges of the cutting parameters used in the test. Other parameters of the cutting system and the measuring rig were kept the same. The experimental results obtained in this test show that no force variation has been observed over a considerably wide range of cutting conditions. This result can be explained as follows: in face cutting, the cutting speed is not constant but differs for

Workpiece

v

4 x 3 f

f Tool

(a)

(b)

Fig. 2.19. (a) Face cutting and (b) the trajectory of the cutting tool (after Astakhov [8]).

Energy Partition in the Cutting System

109

Table 2.5. Ranges of values of cutting parameters for the end turning tests. Parameter Workpiece diameter (mm) Cutting speed of the workpiece (o.d.)* (m/s) Feed (mm/rev) Depth of cut (mm)

Low value

High value

60.00 0.15 0.07 0.10

120.00 4.00 0.25 3.00

*Outer diameter.

each successive point of the tool trajectory (Fig. 2.19b). Therefore, the thermal wave generated on the neighboring trajectory of the cutting tool (Point 3) does not affect the cutting force (energy consumption) on the current trajectory (Point 4), because this thermal wave has been formed at different cutting speeds and, therefore, the deformation and the thermal waves are not coherent. Hence, the results prove that, on the one hand, the cutting speed affects the wavelength, while on the other hand, the interaction of the energy waves is a real phenomenon of the cutting process. The correlation of the wavelengths under different cutting speeds that result in the maximum reinforcement of the coherent waves can also be established using the following considerations. It follows from Eqs. (2.69) and (2.70) that, if the cutting feed is kept constant, the reinforcement (constructive interference) and destructive interference of the total energy flux are possible only when the wavelength is a function of the cutting speed, i.e. when l0 = f(ν) is the case. If a certain ith crest of this function takes place when f = kli , then the next crest appears when the number of waves increases by 1, i.e. when f = (k + 1)li+1 . Consequently, if the cutting force varies according to a sinusoidal function with the cutting speed, li+1 =

li 1 + li /f

(2.80)

Influence of cutting feed When the path difference (the cutting feed) remains constant, a change in the cutting speed causes a periodic increase and decrease of the cutting force due to the variation in the frequencies of the energy waves generated at different cutting speeds (the velocity of deformation). If this happens due to the interference of the energy waves discussed, a change in the cutting feed should also affect the cutting force because the cutting feed defines the path difference. However, force Fz is affected not only by the wave-interaction force component Fs (f ) but also by the force component F0 (f ), which depends on the uncut chip thickness because the uncut chip thickness changes with the cutting feed [2]. Mathematically, it can be represented by analogy with Eq. (2.75) as    2π  Fz = F0 (f ) + Fs (f ) = F0 (f ) + Fa sin (2.81) f + fph l If the wavelength lν1 of the sine wave which approximates the variation in the cutting force Fz with the cutting speed ν and the frequency of the coherent waves l1 are

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Tribology of Metal Cutting

known for the cutting speed ν1 accounting Eq. (2.80), then the wavelength lk for any other cutting speed which differs from ν1 by a number divisible by l1 can be found as follows: lk =

fl1 , f + l1 (k − 1)

where

k = 2, 3 . . . n

(2.82)

Points (li , νi ) calculated using Eq. (2.82) can be approximated by a line so that the wavelength of the deformation wave corresponding to any cutting speed can be calculated knowing ν1 , lν1 and l1 (providing that cutting feed f remains invariable) as l=

1 1/l1 + (ν − ν1 )/(flν1 )

(2.83)

The third series of experiments was carried out using the same experimental conditions. The workpiece diameter was 88 mm, the depth of cut dw = 0.1 mm. The cutting force Fz was measured as a function of the cutting feed f for different speeds of rotation of the workpiece n. The experimental results for ν = 2.9, 2.3, 1.8, 1.4, 1.2 and 0.9 m/s are shown in Table 2.6. The graphical analysis of the experimental results shown in Table 2.6 showed that the maximum and minimum of Fz locate in the “f −Fz ” coordinate system on two inclined parallel lines. Therefore, the mean of the sine wave (for the experimental conditions

Table 2.6. Experimental results (Series No. 3 of experiments). f (mm/rev)

ν = 2.9 m/s Fz (N) Ps (N)

0.070 0.074 0.084 0.097 0.110 0.120 0.130

75 84 81 94 103 103 112

−2.84 3.91 −4.70 1.00 2.68 −2.94 0.40

F0 = 38.5 + 562f f (mm/rev)

0.070 0.074 0.084 0.097 0.110 0.120 0.130 F0 = 10 + 567f

Ps (N) −2.81 4.29 2.37 −1.25 2.63 −3.04 4.41

−3.05 −2.06 2.29 −1.06 −2.53 −0.05 2.42

56.2 60.0 71.2 76.9 84.4 93.7 103.1

ν = 1.8 m/s Fz (N) Ps (N) −0.01 1.67 2.11 1.00 −1.98 2.21 2.26

56.2 60.0 65.6 71.2 75.0 84.4 90.0

F0 = 11 + 690f

F0 = 20 + 518f

ν = 1.2 m/s

ν = 0.9 m/s

ν = 1.4 m/s Fz (N)

0.070 0.074 0.084 0.097 0.110 0.120 0.130

ν = 2.3 m/s Fz (N) Ps (N)

Fz (N) 54.4 58.1 61.9 71.2 75.0 78.7 93.7

Ps (N) 2.11 3.40 1.05 2.48 −1.74 −4.07 4.82

F0 = 9.5 + 611f

Fz (N) 56.2 56.2 52.5 76.9 80.6 88.1 96.6

Ps (N) 3.98 1.54 −8.32 8.11 3.92 5.30 6.69

F0 = 9.5 + 611f

Energy Partition in the Cutting System

111

considered) is a straight line F0 (f ) = C1 + C2 f . Constants C1 and C2 were determined using the experimental data and so the position of the sine wave means were determined for each test (Table 2.6). Then, using Eq. (2.81), the sinusoidal component of Fz was calculated as Fs (f ) = Fz (f ) − F0 (f )

(2.84)

The experimental points for each cutting (deforming) speed were placed in the “f −Fz ” coordinate system. Then a sine wave was found using a specially developed curve-fitting program for the best approximation of the experimental points. Some results are shown in Fig. 2.20. As such, for the cutting speeds in Table 2.6, the wavelengths of the energy waves (deformation and thermal) were determined. The results are as follows: 6.3, 6.5, 7.0, 7.6 and 7.8 µm. To confirm the validity of Eq. (2.83), the initial cutting speed was selected to be ν1 = 0.9 m/s and thus lν1 = 0.56 and lν = 7.8 µm. Using Eq. (2.83), the wavelengths for other cutting speed were calculated with the following results: 6.336, 6.723, 7.033, 7.348 and 7.780 µm. A fairly good agreement between the calculated and the experimentally obtained results proves that in solids, energy expands into waves. The wavelength of these waves depends on the velocity of deformation and can be determined experimentally. Moreover, a comparison of these results with the frequency of chip formation obtained for the same conditions (Fig. 1.43) shows that the chip formation process generated these waves. To prove that the parameters of the waves do not correlate with the rotational speed of the workpiece or with other velocities of the moving parts of the machine tool, a special

n=2.9m/s

−10 10

n=2.3m/s

Force, Ps (N)

−10 10

n=1.8m/s

−10 10

n=1.4m/s

−10 10

n=1.2m/s

−10 10

n=0.9m/s

−10 0.07

0.09

0.11

0.13

Feed, f (mm/rev)

Fig. 2.20. Sine wave approximation of the experimental data in the coordinate system “f – Fz ” (after Astakhov [8]).

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Tribology of Metal Cutting

test was carried out. It was found from the previous experiments that parameters F0 and νph are very sensitive to even small changes in the cutting process [2]. On the contrary, parameters Fa and lν depend only on the cutting regime. Accounting for these facts, the methodology of the current experiment was developed as follows. A stepped workpiece having shoulders of different diameters was first turned on at the smallest diameter using a cutting speed of 2.4 m/s and the parameters Fa1 and lν1 were determined for this case. Then, the next shoulder was turned keeping the same setup and cutting speed by reducing the spindle rotational speed (n (rpm)). As such, the parameters Fa2 and lν2 were calculated using, experimental results. Then, the third shoulder of greater diameter was machined keeping the same conditions including the cutting speed (thus smaller rpm). Again, the parameters Fa3 and and lν3 were determined. Because these parameters were found the same for all the three runs, it was concluded that they depend only on the cutting speed and do not correlate with testing particularities. Proposed methodology of evaluation of cutting force measurements. In order to apply the findings discussed in the practical determination of the cutting force, the following steps are recommended: Step 1: The first series of tests is to be conducted varying the cutting speed ν and measuring the cutting force Fz . As a result, a number of points (νi , Fzi ) are obtained. Step 2: The experimental points are entered into a computer and are placed in the coordinate system ν − Fz . A curve-fitting program is used to approximate them with a sine wave with reasonable accuracy. It is accomplished numerically and/or graphically. Equation (2.75) describes this sine wave as   2π  Fz = Fz0 + Fza sin ν + νph , lv 

(2.85)

where Fz0 is the mean of the sine wave Fz0 =

Fz−max + Fz−min , 2

(2.86)

Fza =

Fz−max − Fz−min , 2

(2.87)

where Fza is its amplitude

where lν and νph are its wavelength and initial phase, respectively. Step 3: The second series of cutting tests is conducted. In this series, N points (N = 1 . . . n) corresponding to different cutting speeds are used. In each point, a number of tests using different cutting feeds are conducted measuring the cutting force Fz . Step 4: The experimental results of Step 3 are entered into the computer. Then, N coordinate systems “f−Fz ” (one for each cutting speed used in the tests) are formed and the experimental points corresponding to different cutting feeds are placed in each of

Energy Partition in the Cutting System

113

these systems. Using Eqs. (2.81) and (2.84), one can find the wavelength of the energy waves for each of the cutting speed used in the tests. Step 5: Using the experimental results of Step 4 for N = 1 and lv determined in Step 1, and, using Eq. (2.83), the wavelengths of the energy waves for the cutting speed used at Points 2 . . . N are calculated. Step 6: The wavelengths obtained at Steps 4 and 5 are compared. The parameters of sine waves obtained in Step 4 are corrected in an iteration procedure until a fairly good agreement of the wavelengths obtained in Steps 4 and 5 is achieved. Importance of the interaction of deformation and thermal waves in metal cutting. The high energy rate and cyclic nature of the chip formation process in metal cutting result in the generation of deformation and thermal waves. Because these waves are generated by the same source, namely, the chip formation process (cutting tool), they are coherent and their interference takes place in the cutting process. This interference affects the amount of external energy required since, according to the von Mises’ criterion of failure with physical meaning given by Hencky, the critical value of the distortion energy (the total strain energy per unit volume) is constant for a given workpiece material. The revealed existence of interference explains the unexplained phenomena of the metal cutting process: • Great scatter in the reported data on cutting force. Even under similar cutting conditions and with extraordinary care while performing the experiments, scatter in cutting force measurements exceeds 50% (for example, [53]). • Foundation of high-speed machining. When the cutting speed increases, the volume of work material removed per unit time also increases so that the energy spent in cutting should increase. Moreover, an increase in the cutting speed leads to the corresponding increase in the strain rate in the chip formation zone. According to Oxley [54], this rate is in the range from 103 to 105 s−1 , or even higher in metal cutting (discussed in Chapter 1). The available data on materials testing at high strain rate (for example, [55]) show that the shear flow stress increases dramatically for many common materials when the rate of strain exceeds 104 . Knowing these facts, one might expect a significant increase in the cutting force when the cutting speed increases. Particularly, the difference should be very significant at high cutting speeds in the so-called high-speed machining. The practice, however, shows that opposite is the case. Zorev [12] studied a number of work materials (from low- to high-carbon steel, low and high alloyed steels) at low and high cutting speeds and conclusively proved that the cutting force decreases (at different rates for different work materials) with an increase in the cutting speed. Moreover, the results of multiple studies on the cutting force in high-speed machining (for example, [15,16]) show a significant decrease (30–40%) in the cutting force at high cutting speed and thus rates of strain. The results presented in this chapter resolve this contradiction. When the cutting speed increases, the time interval between the two successive tool positions (Points 1 and 2 in Fig. 2.15) decreases. As such, higher thermal energy adds to the total energy needed for the fracture of the layer being removed. As a result, the cutting force decreases. Poor reproducibility of the high-speed machining

114

Tribology of Metal Cutting results and the inability to reproduce the results obtained by other researchers [56] can easily be explained by the wave interference phenomena described.

• Inconsistency in tool life. The resource of the cutting tool is defined later in Chapter 4 as the amount of energy that can be transmitted through the cutting wedge (defined as a part of the tool located between the rake and the flank contact areas) until it fails [6]. Great inconsistency in tool life, known to the specialists in the field, can be easily explained by the wave phenomena described because the energy transmitted through the cutting wedge depends on the interaction of the deformation and thermal waves in the machining zone. The results obtained offer a novel approach in the selection of optimal cutting regime in machining, particularly high-speed machining. This regime should be selected so that the constructive interference of energy waves results in their maximum reinforcement to reduce the energy needed to accomplish the process and to increase the tool life. At higher strain rates and cutting speeds, the benefits of the proposed approach are more significant.

2.7.2 Method 2: using the appropriate state of stress As discussed above, the state of stress in the layer being removed is triaxial even in the simplest method of machining – orthogonal cutting. As known [57], the state of stress in the body, which undergoes plastic deformation, affects the fracture strain. For example, it is known that hydrostatic compression increases the fracture strain and tension decreases the fracture strain [58]. However, this general knowledge is not sufficient to control the deformation process. Therefore, a certain generalized parameter characterizing the state of stress should be selected to study the correlation between the state of stress and the fracture strain. One of the most versatile and physically sound criteria for the characterization of the state of stress in plastic deformation of engineering materials is Π − a criterion defined as [57] 3I1 (σ) Π=  , 2 I12 (σ) − 3I22 (σ)

(2.88)

where I1 (σ) and I2 (σ) are the first and the second stress invariants that is expressed in terms of the principal stresses σ1 , σ2 and σ3 as I1 = σ1 + σ2 + σ3

(2.89)

I2 = − (σ1 σ2 + σ2 σ3 + σ3 σ1 )

(2.90)

Figure 2.21 shows the relationships between the strain at fracture and the state of stress represented by Π factor. As shown, the strain at fracture and thus the energy needed for the separation of the layer being removed significantly depend on the state of stress for a wide variety of work materials. It is also shown in Fig. 2.21 that different work

Energy Partition in the Cutting System

115

εf 3.0

12 1

2.0

13 2 6

1.0

7

5

0.5

4

3

9 11 10

8

0.2

0.1 −8

−8

0

4

8

Π

Fig. 2.21. Effect of stress triaxiality represented by the Π criterion on the strain at fracture: 1 – niobioum, 2 – iron, 3 – tungsten, 4 – molybdenum, 5 – beryllium, 6 – magnesium, 7 – zinc, 8 – tin alloy, 9 – brass, 10 – brass alloy, 11 – strain-hardened and 12 – cast lead (after Astakhov [2]).

materials have different sensitivity to the stress triaxiality. This fact is well known in material testing [59,60]. The state of stress in the deformation zone depends primarily on the tool geometry so that, by proper selection of the tool geometry according to the properties of the work material, one can achieve significant reduction in the energy spent in machining. In this respect, the importance and significance of the cutting tool geometry (Appendix A) can be appreciated for the first time as having defined the physical sense as this geometry forms this state of stress. Since the tool forms a certain hydrostatic pressure in the layer being removed, it is of interest to analyze its influence on the strain at fracture. It was mentioned in [2] that Lode [61] investigated the validity of the yield criteria using some thin-walled tubes made of steel, copper and nickel subjected to various combinations of uniaxial tension and internal hydrostatic pressure. In doing this, he devised a sensitive method to determine the effect of the intermediate principal stress on yielding. This may be explained as follows. Tresca [62] suggested that yielding occurs when the maximum value of the extreme shear stress in the material, equal to half the difference between the algebraic maximum (σ1 ) and minimum (σ3 ) principal stresses, i.e. 1 τmax = τ1 = ± (σ1 − σ3 ) 2

(2.91)

116

Tribology of Metal Cutting

attains a critical value. As shown, the Tresca yield criterion requires the maximum and minimum principal stresses to be known in advance. When applied for yielding in uniaxial tension where σ1 = σy , which is the uniaxial yield stress of the material, σ2 = σ3 = 0, the criterion gives σ1 − σ3 = σy

(2.92)

(σ1 − σ3 ) =1 σy

(2.93)

which, if σ1 ≥ σ2 ≥ σ3 , yields

The intermediate principal stress (σ2 ) can thus vary from its maximum value σ2 = σ1 to its minimum value σ2 = σ3 without apparently affecting the yield criterion expressed by Eq. (2.93). To characterize the influence of the intermediate principal stress (σ2 ) Lode introduced the parameter µL =

2σ2 − σ3 − σ1 σ2 − (σ1 + σ3 )/2 = σ1 − σ 3 (σ1 − σ3 )/2

(2.94)

which is known as the Lode stress parameter [21]. Equation (2.94) can be rearranged so that σ2 =

σ1 + σ3 σ1 − σ 3 + µL 2 2

(2.95)

The von Mises yield criterion in terms of the principal stresses (Eq. (2.12)) can be written as (σ1 − σ2 )2 + (σ2 − σ3 )2 + (σ3 − σ1 )2 = 2σy2

(2.96)

and if σ2 from Eq. (2.95) is substituted, after rearranging and simplifying, the von Mises yield criterion becomes (σ1 − σ3 ) 2 = 1 2 σy 3 + µ2L /

(2.97)

When σ2 = σ3 , Eq. (2.94) shows that µL = −1 and when σ2 = σ1 , µL = +1. Because σ1 ≥ σ2 ≥ σ3 , it follows that −1 ≤ µL ≤ +1. When µL = −1, the principal stresses are σ1 , σ2 = σ3 which is the uniaxial tension (σ1 − σ3 ) with hydrostatic stress σ3 . When µL = +1, the principal stresses are σ1 = σ2 , σ3 , which is the uniaxial compression. In addition to the stress parameter (µL ) defined by Eq. (2.94), Lode also introduced the plastic strain parameter, υL , defined as
 p p p p p p dε2 − 1 2 dε3 + dε1 2dε2 − dε3 − dε1 
 υL = = , (2.98) p p p p dε3 − dε1 1 2 dε3 − dε1

Energy Partition in the Cutting System p

p

117

p

where dε1 , dε2 and dε3 are the plastic strain increments in the principal directions. Analyzing stress–strain relations proposed by Prandtl for plane strain deformation, Reuss [63] assumed that the plastic strain increment is, at any instant of loading, proportional to the instantaneous stress deviation and the shear stress such that p

p

p

p

p

p

dεy dγxy dγyz dεz dγzx dεx =  =  = = = = dλ  σx σy σz τxy τyz τzx

(2.99)

or, more compactly, in tensor notation dεij = σij dλ, p

(2.100)

where σij is the deviator stress tensor, dλ is a scalar non-negative constant of proportionality which is not a material constant and may vary throughout the stress history. As before, the superscript “p” denotes the plastic strain increment. Considering the principal directions, Eq. (2.100) can be stated as p

p

p

dε dε dε1 = 2 = 3 = dλ  σ1 σ2 σ3

(2.101)

If Eq. (2.101) is valid, µL should be numerically equal to υL . It directly follows from Eqs. (2.101) and (2.95) that p

υL =

p

p

2dε2 − dε3 − dε1 p

p

dε3 − dε1

=

2σ2 − σ3 − σ1 2σ2 − σ3 − σ1 =   σ3 − σ 1 σ1 − σ 3

(2.102)

Thus υL = µL . To prevent confusion, it should be appreciated that the Lode strain parameter υL is not related to Poisson’s ratio [21]. A generalization of the available experimental material on deformation of metals results in the following conclusions [2]: • Failure strain depends significantly on the characteristic of the state of stress, as shown in Fig. 2.21. Therefore, by changing this state, the fracture strain and thus the energy consumption per unit volume of the layer being removed in cutting can be minimized. In the author’s opinion, the easiest way to do this is to change the geometry of the cutting tool used to achieve the necessary µL . This approach appears to be a new ground for selecting both the cutting geometry and the cutting regime. • The dependence of the fracture strain εf on the hydrostatic stress ph may be characterized by three distinct zones (Fig. 2.22): (I) zone of insignificant dependence, wherein εf is independent or depends insignificantly on ph until a certain limit phI . This behavior is observed in tensile tests of brittle materials (cast iron, chromium);

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Tribology of Metal Cutting

ef

I

II

phI

III

phII

ph

Fig. 2.22. Generalized dependence of the fracture strain (εf ) on the hydrostatic stress (ph ) (after Astakhov [2]).

(II) zone of significance, approximately linear, dependence. This behavior was observed in the testing of all the metals; (III) zone of a parabolic increase in plasticity. The boundary between the zones II and III (the limit phII ) is not one line as shown in Fig. 2.22. Rather, it is a small zone. The exact behavior of metals in the zone III is not yet known.

ef

0.4 q = 700°C

0.3

0.2 q = 250°C 0.1 −mL

−0.5

0

0.5

+mL

Fig. 2.23. Effect of temperature on the influence of the Lode parameter (µL ) on the fracture strain (εf ) (after Astakhov [2]).

Energy Partition in the Cutting System

119

s

sUTS

−∆sm +∆sm

qpl ∆sm

∆sm

tan qpl

tan qpl

( ∆ll ) 0

f

∆l l0

Fig. 2.24. Determining the stress and elongation at fracture for different stressed states.

• The temperature under which the test is carried out has a significant influence on the fracture strain. However, over the range of temperatures in the deformation zone (high tool–chip contact temperatures do not affect the resistance of the work material to cutting), temperature may not significantly affect the dependence of the fracture strain on the Lode stress parameter, as illustrated in Fig. 2.23. • Although the influence of superimposed hydrostatic pressure on the deformation and fracture behavior of work materials is very significant, a concern which remains is the practical determination of this influence. In other words, the question can be rephrased as: “Should one carry out a series of materials tests over a wide range of hydrostatic pressures?” In the author’s opinion, it is not feasible because a bulk of data obtained using special testing equipment (for example Material Testing System (MTS)) has to be generated. Obviously, it may take years to collect these data. Therefore, a much more practical way should be suggested. One of the most promising directions in this respect is use of available tensile data to calculate the strain and stress at fracture at different states of stress. Brownrigg et al. [64] proposed the following relationship εf (ph ) 1.68ph =1+ , εf (0) 2σ¯

(2.103)

where εf (ph ) is the fracture strain at superimposed hydrostatic pressure ph , εf (0) is the fracture strain in uniaxial tension with no additional superimposed pressure and σ¯ is the effective stress at fracture [60].

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Tribology of Metal Cutting

Oh [65] proposed a simple method that, in the author’s opinion, can be used to the first approximation to determine the stress and strain at fracture under different state of stress. The essence of this method is shown in Fig. 2.24 (bilinear representation of elongation–stress diagram) is self evident. As such the elongation at fracture is calculated as       ∆l ∆l −1 ∆σm , = + (2.104) l0 f , ∆σm l0 f tan θpl where



∆l l0 f , ∆σ m

is the elongation at fracture at mean stress variation ∆σm ,





∆l l0 f

is the elongation at fracture in uniaxial tension with no additional superimposed pressure.

References [1] Bhushan, B., Principles and Applications of Tribology, John Wiley & Sons, New York, 1999. [2] Astakhov, V.P., Metal Cutting Mechanics, CRC Press, Boca Raton, USA, 1998. [3] Astakhov, V.P., Chapter 9: Tribology of metal cutting, in Mechanical Tribology. Material Characterization and Application, G.T.a.H. Liang, Editor. MarcelDekker, New York, 2004, pp. 307–346. [4] Astakhov, V.P., A treatise on material characterization in the metal cutting process. Part 2: Cutting as the fracture of workpiece material, Journal of Materials Processing Technology, 96 (1999), 34–41. [5] Astakhov, V.P., The assessment of cutting tool wear, International Journal of Machine Tools and Manufacture, 44 (2004), 637–647. [6] Komarovsky, A.A., Astakhov, V.P., Physics of Strength and Fracture Control: Fundamentals of Adaptation of Engineering Materials and Structures, CRC Press, Boca Raton, USA, 2002. [7] Astakhov, V.P., Shvets, S.V., A system concept in metal cutting, Journal of Materials Processing Technology, 79 (1998), 189–199. [8] Astakhov, V.P., Shvets, S.V., A novel approach to operating force evaluation in high strain rate metal-deforming technological processes, Journal of Materials Processing Technology, 117 (2001), 226–237. [9] Astakhov, V.P., A treatise on material characterization in the metal cutting process. Part 1: A novel approach and experimental verification, Journal of Materials Processing Technology, 96 (1999), 22–33. [10] Ivester, R.W., Kennedy, M., Davies, M., Stevenson, R. J., Thiele, J., Furness, R., Athavale, S., Assessment of machining models: progress report. In Proc. 3rd CIRP Int. Workshop on Modelling of Machining Operations, University of New South Wales, Sydney, Australia, 2000. [11] Dieter, G., Mechanical Metallurgy, McGraw-Hill, New York, 1976. [12] Zorev, N.N., Metal Cutting Mechanics, Pergamon Press, Oxford, 1966.

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[13] Shaw, M.C., Metal Cutting Principles, Third Edition. Massachusetts Institute of Technology Publication, Cambridge, 1954. [14] Oxley, P.L.B., Mechanics of Machining: An Analytical Approach to Assessing Machinability, John Wiley & Sons, New York, USA, 1989. [15] Merchant, M.E., Mechanics of the metal cutting process. I. Orthogonal cutting and a type 2 chip, Journal of Applied Physics, 16 (1945), 267–275. [16] Gorczyca, F.Y., Application of Metal Cutting Theory, Industrial Press, New York, 1987. [17] Stenphenson, D.A., Agapiou, J.S., Metal Cutting Theory and Practice, Marcel Dekker, New York, 1996. [18] Trent, E.M., Wright, P.K., Metal Cutting, Butterworth-Heinemann, Boston, 2000. [19] Altintas, Y., Manufacturing Automation. Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design, Cambridge University Press, Cambridge, 2000. [20] Childs, T.H.C., Maekawa, K., Obikawa, T., Yamane, Y., Metal Machining. Theory and Application, Arnold, London, 2000. [21] Slater, R.A.C., Engineering Plasticity: Theory and Application to Metal Forming Processes, The Macmillan Press Ltd., London, 1977. [22] Klausz, A.S., Klausz, K., ed. Unified Constitutive Laws of Plastic Deformation, Academic Press, New York, 1996. [23] Incopera, F.P., de Witt, D.P., Fundamentals of Heat and Mass Transfer, John Wiley & Sons, New York, 2001. [24] Manca, O., Morrone, D., Nardini, S., Thermal analysis of solids at high Péclet numbers subjected to moving heat sources, ASME Journal of Heat Transfer, 121(1) (1999), 182–186. [25] Muzychka, Y.S., Yovanovich, M.M., Thermal resistance models for non-circular moving heat sources on a half space, ASME Journal of Heat Transfer, 123 (2001), 624–632. [26] Boothroyd, G., Knight, W.A., Fundamentals of Machining and Machine Tools, Second Edition. Marcel Dekker, New York, 1989. [27] Shaw, M.C., Metal Cutting Principles, Second Edition. Oxford University Press, Oxford, 2004. [28] Astakhov, V.P., Shvets, S., The assessment of plastic deformation in metal cutting, Journal of Materials Processing Technology, 146 (2004), 193–202. [29] Ostafiev, V.A., Noshchenko, A.N., Numerical analysis of three-dimensional heat exchange in oblique cutting, Annals of the CIRP, 34 (1985), 137–140. [30] Ostafiev, V., Kharkevich, A., Weinert, K., Ostafiev, S., Tool heat transfer in orthogonal cutting, ASME Journal of Manufacturing Science and Engineering, 121 (1999), 541–549. [31] Reznikov, A.N., Reznikov, L.A., Thermal Processes in Machining Systems (in Russian), Machinostroenie, Moscow, 1990. [32] Yakimov, A.V., Slobodjanik, P.T., Usov, A.V., Thermal Physics of Machining (in Russian), Lybid, Kiev-Odessa, 1991.

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[33] Lacombe, P., Baroux, B., Beranger, G., Les Aciers Inoxidables, Les Editions De Physique, Paris, 1990. [34] Schmidt, A.O., Gilbert, W.W., Boston, O.W., A thermal balance method and mechanical investigation for evaluating machinability, ASME Transactions, 67 (1945), 225–232. [35] Rall, D.I., Giedt, W.H., Heat transfer to, and temperature distribution in a metal cutting tool, ASME Transactions, 78 (1956), 1507–1512. [36] Darwish, S., Davies, R., Investigation of the heat flow through bonded and brazed metal cutting tools, International Journal of Machine Tool Design and Research, 29 (1989), 229–237. [37] Ay, H., Yang, W.J., Yang, J.A., Dynamics of cutting tool temperatures during cutting process, Experimental Heat Transfer, 7 (1991), 203–216. [38] Moufki, A., Dudzinski, D., Molinari, A., Rausch, M., Thermoviscoplastic modelling of oblique cutting: forces and chip flow predictions, International Journal of Mechanical Sciences, 42 (2000), 1205–1232. [39] Maugin, G.A., The Thermodynamics of Plasticity and Fracture, Cambridge University Press, Cambridge, 1992. [40] Moufki, A., Molinari, A., Dudzinski, D., Modelling of orthogonal cutting with a Temperature dependent friction law, Journal of the Mechanics and Physics of Solids, 36 (1998), 2103–2138. [41] Bever, M.B., Marshall, E.R., Ticknor, I.B., The energy stored in metal chips during orthogonal cutting, Journal of Applied Physics, 24 (1953), 1176–1179. [42] Zehnder, A.T., Babinsky, I., Palmer, T., Hybrid method for determining the fraction of plastic work converted to heat, Experimental Mechanics, 38 (1998), 295–302. [43] Atkins, A.G., Modelling metal cutting using modern ductile fracture mechanics: qualitative explanations for some longstanding problems, International Journal of Mechanical Science, 45 (2003), 373–396. [44] Zehnder, A.T., Plasticity induced heating in the fracture and cutting of metals, in Thermo Mechanical Fatigue and Fracture, M.H. Aliabadi, Editor. WIT Press, Southampton, 2002, pp. 209–244. [45] Crafoord, R., Kaminski, J., Lagerberg, S., Ljungkrona, O., Wretland, A., Chip control in tube turning using a high-pressure water jet, Proceedings of the Institution of Mechanical Engineers Part B, 213 (1999), 761–767. [46] Chan, C.L., Chandra, A., A boundary element method analysis of the thermal aspects of metal cutting processes, ASME Journal of Engineering for Industry, 113 (1991), 311–319. [47] Rosakis, P., Rosakis, A.J., Ravichandran, G., Hodoway, J., A thermodynamic internal variable model for the partition of plastic work into heat and stored energy in metals, Journal of the Mechanics and Physics of Solids, 48 (2000), 581–607. [48] Astakhov, V.P., Galitsky, V.V., Osman, M.O.M., A novel approach to the design of selfpiloting drills with external chip removal, Part 2: bottom clearance topology and experimental results, ASME Journal of Engineering for Industry, 117 (1995), 464–474.

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[49] Sears, F.W., Zemansky, M.W., Uoung, H.D., University Physics, Fifth Edition. AddisonWesley, Reading, Massachusetts, 1976. [50] Truesdell, C., Noll, W., The nonlinear field theories of mechanics, in Encyclopedia of Physics, Vol. III/3, S. Flugge, Editor. Springer-Verlag, Berlin, 1965. [51] Engelbrecht, J., Nonlinear Wave Processes of Deformation in Solids, Pitman Publishing Ltd., London, 1983. [52] Kronenberg, M., Machining Science and Application. Theory and Practice for Operation and Development of Machining Processes, Pergamon Press, Oxford, 1966. [53] Ivester, R.W., Kennedy, M., Davies, M., Stevenson, R., Thiele, J., Furness, R., Athavale, S., Assessment of Machining Models: Progress Report, National Institute of Standards and Technology, Gaithersburg, USA, 2000. pp. 1–15. [54] Oxley, P.L.B., Rate of Strain Effect in Metal Cutting, ASME Journal of Engineering for Industry, 85 (1963), 335–345. [55] Follansbee, P.S., Analysis of the strain-rate sensitivity at high strain rates in fcc and bcc metals. In Proceedings of the Fourteenth International Conference on the Mechanical Properties of Materials at High Rates of Strain, Institute of Physics, Bristol, Oxford and New York, 1989. [56] King, R.I., Chapter 1: Historical background, in Handbook of High-Speed Machining Technology, R.I. King, Editor. Chapman and Hall, New York, 1985. [57] Johnson, W., Mellor, P.B., Engineering Plasticity, van Nostrand Reinhold Company, London, Inglaterra, 1973. [58] Scudnov, V.A., Limiting Plastic Deformations of Metals (in Russian), Metallurgia, Moscow, 1989. [59] Helbert, A.L., Feaugas, X., Claver, M., The influence of stress triaxiality on the damage mechanisms in an equiaxed Ti-6Al-4v alloy, Metallurgical and Materials Transactions A, 27A (1996), [60] Biel-Golaska, M., Analyses of cast steel fracture mechanisms for different state of stress, Fatigue & Fracture of Engineering Materials & Structures, 21 (1998), 965–975. [61] Lode, W., Versuch uber den einfluss der mitteren hauptspannung auf das fliessen der metalle eisen, kupfer and nickel, Zeitscrift für Physik, 36 (1926), 913–964. [62] Tresca, H., Sur l’ecoulement des corps solides soumis a de fortes pression, Comptes Rendus Acad. Sci. Paris, Paris, 59 (1864), 754–791. [63] Reuss, A., Beruecksichtigung der elastishchen formaenderungen in der plastizitaetstheorie, Zeitschrift für angewandte Mathematik and Mechanik, 10 (1930), 266–284. [64] Brownrigg, A., Spitzig, W.A., Richmond, O., Teirlinck, D., Embury, J.D., The influence of hydrostatic pressure on the flow stress and ductility of a sperodized 1045 steel, Acta Metallurgica, 31 (1983), 1141–1150. [65] Oh, H.-K., Determination of ductile fracture (ductility) at any stress state by means of the uniaxial tensile test, Journal of Material Processing Technology, 53 (1995), 582–587.

CHAPTER 3

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

3.1 Introduction This chapter considers the tribology of the tool–chip and tool–workpiece interfaces, namely, the distribution of contact stresses, nature and interdependence of contact processes, correlations between characteristics of the contact process with important input and output parameters and characteristics of the cutting process. Particular attention is paid to the properties of the tool and work materials. The tool–chip and tool–workpiece interfaces are those contact areas that directly participate in the cutting process. Considerably different functions of the tool–chip and tool–workpiece interfaces in this process define the differences in the tribological processes at these interfaces. Although there are a number of differences, there are also a number of similarities in the tribology of these interfaces as high contact pressures and temperatures, contact with freshly formed ( juvenile) counter-surfaces and high sliding velocities. There is also a correlation between the stresses at these interfaces as they both are related to the same state of stress in the deformation zone. As such, however, the tool–chip interface plays a leading role that defines to a large extent this state. Therefore, a greater part of the considerations presented in this chapter is dedicated to the tribological conditions at the tool–chip interface. The major results of Chapter 2 show that only 30–50% of the energy required by the cutting system is spent for the useful work, i.e. for the separation of the layer being removed from the workpiece. The rest is spent at the tool–chip and tool–workpiece interfaces. This fact can be easily appreciated if one realizes that nearly all the energy spent in the cutting process is converted into thermal energy. Therefore, the temperature of a certain zone in the cutting system is a very good and relevant indicator of the energy spent in this zone as this energy generates heat, so the higher the temperature of a particular zone, the greater is the energy spent in this zone. If one compares the temperature in the deformation zone and that at the discussed interfaces, one can come to a surprising yet well-known conclusion. The essence of it is that the temperature in the deformation zone, where the major 124

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

125

work of plastic deformation and separation of the layer being removed from the rest of the workpiece takes place, is relatively low (normally 80–250◦ C) as discussed later in this chapter. On the contrary, the maximum temperatures at the tool–chip interface can reach more than 1000◦ C. Therefore, more energy required by the cutting system is spent at the tool–chip and tool–workpiece interfaces although the deformation zone prevented much more attention of the researchers in the field. The main objective of this chapter is to discuss the tribological conditions at the tool– chip and tool–workpiece interfaces. The understanding of these conditions and the proper utilization of this understanding in the design of the cutting process should result in the increased efficiency of the cutting system and in the reduction of tool wear. These results can be used in the meaningful selection of the machining regime, tool geometry and tool materials (including coatings).

3.2 Tool–Chip Interface When a metal is cut, the cutting force acts mainly through a small area of the rake face, which is in contact with the chip and thus, is known as the tool–chip interface. Therefore, it is of interest in determining the cutting force, developing the theory of tool wear and understanding the mechanics of chip formation to establish the tribological characteristics of the tool–chip interface. The basic tribological characteristics of the tool–chip interface are: • The contact length – the length of the tool–chip contact, lc , • The sliding velocity, ν1 = ν/ζ, • The friction force at the tool–chip interface, F , • The specific frictional force which is the mean shear stress, τc =

F lc dw1 ,

• The normal force at the tool–chip interface, N, • Mean normal stress at the tool–chip interface, σc =

N lc dw1 ,

• Mean contact temperature at the tool–chip interface, θr−av .

3.2.1 Friction coefficient In Merchant’s analysis, it is implied that the contact between the tool and the chip is a sliding contact, where the coefficient of friction is constant [1]. In most engineering and physical situations, friction effects at a tribological interface are described by a constant coefficient of Coulomb friction µf , µf =

F , N

(3.1)

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Tribology of Metal Cutting

where N is the normal force acting at the considered interface (Fig. 1.7) and F is the frictional force at this interface (Fig. 1.7). Although it is well established that contact between the two bodies is limited to only a few microscopic high points (asperities), it is customary to calculate the stresses by assuming that the forces are distributed over the total (apparent) contact area. Such an approximation, however, is not far from reality in machining, where the actual and apparent contact areas are practically the same due to high contact pressures [2]. If it is so, the numerator and denumerator of Eq. (3.1) can be divided over the tool–chip contact Ac and then recalling that the mean normal stress at the interface is σc = N/Ac and the mean shear (frictional) stress at the interface is τc = F/Ac , one can obtain µf =

τc σc

(3.2)

Equation (3.2) reveals that if the friction coefficient at the tool–chip interface is constant, the ratio of the shear and normal stresses should be the same along the entire contact length. As discussed by Dieter [3], the above analysis was for sliding friction at the interface, as in our first encounter with friction in elementary physics. At the other extreme, we can envision a situation where the interface has a constant film shear strength. The most usual case is sticking friction, where there is no relative motion between the chip and the tool at the interface. For sticking friction, this shear strength should be equal to the flow stress in shear, kc , and the normal stress to the yield stress of the work material σy . Using the von Mises yield criterion, the coefficient of friction under sticking conditions is
√ 3 σy kc = = 0.577 µf = σy σy

(3.3)

Therefore, the value of the friction coefficient µf defined by Eq. (3.3) should be considered as the limiting value so that if µf ≥ 0.577, no relative motion can occur at the interface. In the practice of metal cutting, however, this is not the case. In experimental studies, Zorev [2] obtained µf = 0.6–1.8, Kronenberg [4] – 0.77–1.46, Armarego and Brown [5] – 0.8–2.0, Finnie and Shaw [6] – 0.88–1.85, Usui and Takeyama [7] – 0.4–2.0, etc. In the simulations of metal cutting, Stenkowsky and Moon [8] used µf = 0.2, Komvopoulos and Erpenbeck [9] – 0.0–0.5, Lin, Pan and Lo [10] – 0.074, Lin and Lin [11] – 0.001, Stenkowsky and Carroll [12] – 0.3, Endres, DeVor and Kappor [13] – 0.05, 0.10, 0.25, and 0.5, Olovsson, Nilson and Simonsson [14] – 0.1, etc. As seen, the reported values of µf obtained in metal cutting tests are well above 0.577. On the other hand, the values of µf used in modeling (more often in FEM modeling), are always below the limiting value to suit the sliding condition at the interface. Interestingly, the results of FEM modeling were always found to be in good agreement with the experimental results regardless of whether the particular value of the friction coefficient is selected for such a modeling.

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

127

It is true that, in general, the coefficient of friction for sliding surfaces remains constant within wide ranges of the relative velocity, apparent contact area and normal load. In contrast, in metal cutting, the coefficient of friction varies with respect to the normal load, the relative velocity and the apparent contact area. The coefficient of friction in metal cutting was found to be so variable that Hahn [15,16] doubted whether this term served any useful purpose. Moreover, Finnie and Shaw [6] have concluded that the concept of the coefficient of friction is inadequate to characterize the sliding between chip and tool and thus recommended to discontinue using the concept of the coefficient of friction in metal cutting. An extensive analysis of the inadequacy of the concept of the friction coefficient in metal cutting was presented by Kronenberg (pp.18–25 in [4]) who stated “I do not agree with the commonly accepted concept of coefficient of friction in metal cutting and I am using the term ‘apparent coefficient of friction’ wherever feasible until this problem has been resolved.” Unfortunately, it has never been resolved although more than 40 years have passed since this statement of Kronenberg. To model friction conditions in metal cutting and thus to determine the real value of the friction coefficient, a large number of theoretical analyses [17–31] have been carried out to determine the influence of various parameters on the interfacial friction. Despite the improvements made in the modeling of friction in machining processes over the last 30 years, there are still a number of limitations so that the results of these studies are hardly applicable to metal cutting. In the author’s opinion, the most severe drawbacks of the discussed theoretical considerations are: • At the interface, the soft material is always assumed to be rigid, perfectly plastic, incompressible and isotropic at all stages of deformation. Moreover, no superficial and in-depth residual stresses due to previous deformation can be accounted for. Obviously, this is not the case in metal cutting and particularly at the tool–chip interface. • The approaches known so far consider only two-dimensional asperity interaction ignoring the three-dimensional nature of asperities and actual multi-asperity interaction. The shape of the asperity should be well defined so that its initial and final point should lie on the same line parallel to the direction of relative motion. Moreover, this shape determines the slipline field where the discontinuity of tangential velocity leads to infinite calculated strains. No wonder the chip formation model predicts an increase in the coefficient of friction with improved lubrication [22]. • The sliding speed was not considered to be an important factor. The temperature and strain rate effects are poorly accounted for. The sliding speed even in the verification experiments was 0.3 mm/s and this is obviously way below the sliding speeds found at the tool–chip interface. It was also found that the strains determined from the experimental flow fields are significantly lower than those calculated from the model [25]. A number of experimental techniques and tests for evaluating the interfacial friction in metal cutting have been developed. Many of these tests actually aim to evaluate properties of the metalworking fluids and thus are known as the lubricity tests [32]. Each has its

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own inherent advantages and limitations. Lubricity tests can be broadly divided into three groups [32]. One group is based upon simple rubbing or rolling action. Another group is based upon metal removal or chipmaking processes. The final group incorporates forming or drawing of a metal sheet. It was soon recognized, however, that, because of the complexity of field conditions, no simple test machine can simulate the lubrication requirements for different machining operations. Therefore, it is rather difficult, or even impossible, to correlate bench test data with the actual performance [32]. To understand the problem with experimental determination of the friction coefficient, one should refer to the force diagram developed by Merchant [1] and shown in Fig. 1.1(a). Since Merchant assumed Coulomb friction is the case in metal cutting, the following expression for the friction coefficient was obtained from the force diagram shown in Fig. 1.1(d) µ=

F FT + FC tan γ = N FC − FT tan γ

(3.4)

It directly follows from Eq. (3.4) that the friction coefficient can be calculated using the friction and normal forces obtained experimentally by resolving the measured cutting and trust components of the cutting force. The friction coefficient thus obtained does not match with common experience. This was first found by Kronenberg in 1927 (p.18 in [4]). Unfortunately, Merchant, who conducted his research 20 years later, did not pay attention to the first edition of Kronenberg’s book.

3.2.2 Contact stresses distribution – reported results Later research has been aimed at obtaining a better understanding of the conditions at the tool–chip interface by studying the distribution of the normal and shear stress at this interface. A variety of experimental techniques including photoelastic tools, splittool dynamometer, transparent tool for the direct observation of the tool–chip interface, metallurgical examination of “quick-stop” chip-section including experimental slipline field method have been developed [2,33–39]. Photoelastic method. The pioneers in the field of photoelastic analysis of orthogonal metal cutting, such as Coker and Filon [40] and Zeichev [41] have generally used a photoelastic work material in their studies. This has shortcomings as the work material undergoes plastic deformation as shown by Frocht and Thomsen [42] and Ocushiri and Fukuii [43] who have used a photoelastic material as a cutting tool, which was pressed against the already-made chip. Andreev [44] and Kattwinkel [45] were probably the first scientists who obtained some meaningful stress distributions at the tool–chip interface using a photoelastic tool [38]. Andreev [44] pointed out that the whole contact length lc is divided into two distinctive parts of approximately equal length: the plastic part that extends from the cutting edge to the middle of the contact length (or the length of the tool–chip interface) and the elastic part from the middle of contact to the point of chip separation from the

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

3

1

5 4

Normal stress

129

6

(a) 2

0

0

0.5lc Distance from the cutting edge

6 4

lc

5

Shear stress

3

(b)

1 2

0 0

0.5lc Distance from the cutting edge

lc

Fig. 3.1. Stress distributions at the tool–chip interface reported in literature: (a) normal stress and (b) shear (tangential) stress (after Astakhov and Outeiro [73]).

tool–rake face. The results obtained indicate that the normal stress, being zero at the point of chip separation, increases exponentially towards the cutting edge (curve 1, Fig. 3.1(a)). The distribution of the shear stress obtained by Andreev is shown in Fig. 3.1(b), curve 1. Kettwinkel, using a similar experimental technique, obtained similar distribution of the normal stress (curve 1, Fig. 3.1(a)). He found, however, that the shear stress, after reaching the maximum value at the middle of the contact length then decreases toward the cutting edge (curve 2, Fig. 3.1(b)). Takeyama and Usui [46] studied the stress distribution along the tool–chip interface by measuring the cutting forces on tools with various contact lengths. Their result for the normal stress is shown by curve 2 in Fig. 3.1(a) and for the shear stress by curve 3 in Fig. 3.1(b). Later on, Usui and Takeyama [7] improved the accuracy of their experiments and thus concluded that the distribution of the normal stress is as shown by curve 3 in Fig. 3.1(a) and that of the shear stress is as shown by curve 4 in Fig. 3.1(b). The same experimental technique was used by Chandrasekaran and Kapoor [47]. Trying to understand the influence of tool geometry, they used photoelastic tools of different rake angles.

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Tribology of Metal Cutting

They found that the contact length lc is inversely proportional to the rake angle. For positive rake angles (0, 10 and 20◦ ), the distribution of the shear stress corresponds to that given by curve 3 in Fig. 3.1(b) but when the rake angle was negative, the distribution given by curve 5 in Fig. 3.1(b) was the case. For all the studied tools which had positive rake angles, the maximum of the shear stress was found to be very nearly that of the shear yield strength of the work material. In their opinion, a significant difference in the curves of normal stress distribution shows (curve 4 corresponds to a +20◦ rake angle, curve 5 corresponds to –10◦ ) that there is some pronounced differences in the case of a negative rake tool. Further studies using photoelastic tools [48,49] yielded different results. Amini [48] concluded that both the normal and the shear stresses increase in a non-linear manner from the point of chip separation towards the cutting edge. Ocusima et al. [49] found that the shear stress distribution is similar to that of the given by curve 1 in Fig. 3.1(b) and remains constant over approximately two-thirds of the contact length lc . The normal stress, being approximately equal to the shear stress at the cutting edge, reaches its maximum at the mid point of the contact length and then decreases gradually to zero (curve 6 in Fig. 3.1(a)). Although the above-discussed experimental studies using the photoelastic method were great attempts to determine the stress distributions during machining, a number of points of criticism on these results remain open. The major concerns are with the cutting speeds used in the test which are thousand times lower (due to extremely low hot hardness of the tools used) than those found in practice. As a result, there is no ground to believe that the real tribological characteristics of the tool–chip contact, namely the mode of deformation; the maximum temperature and temperature distribution; relative velocity of the contacting bodies; abrasion, adhesion, diffusion, and chemical interactions [39], would be even close to those in these studies. Moreover, it is not possible to determine accurately the contact stresses immediately adjacent to the cutting edge because the contact stresses at the tool flank cause distortion of the isochromatic fringes in this region [50]. Bagchi and Wright [37,51] overcame the problem with tool hot hardness by using a single crystal sapphire tool although the stress birefringence effect in sapphire is relatively weak and, of course, sapphire is inherently brittle. Despite these difficulties, they were able to machine steel and brass specimens at speeds of up to 75 m/min and at a maximum feed rate of 0.381 mm/rev to study the effect of speed and feed on stress distributions [37]. It was found that the normal and shear stress distributions qualitatively resemble those obtained by Chandrasekaran and Kapoor [47]; the cutting speed does not have significant influence on the peak normal stress while the feed and the uncut chip thickness do. Split tool method. The method was first completely described and used by Loladze [37,52,53]. The method is based on the use of a composite cutting tool having the cutting wedge divided into two parts. The principles of design of the split tool is shown schematically in Fig. 3.2. The cutting wedge and thus, the tool rake face is divided into two parts, namely T1 and T2 . During the test, the forces acting only on the part T1 were measured. During the experiment, the length of T2 was incrementally increased from the smallest possible value up to lc .

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

Cutting direction

131

FNi Chip

Ffi

li lc T1 T2

Fig. 3.2. Principle of measurement of stress distribution using the split tool technique.

The determination of the stress distribution consists of the following steps: • A cutting test is carried out with the part T2 having length li , and the normal FNi and frictional Ff i forces acting on this part are measured. • The length li is decreased to li+1 and the next test is carried out under the same cutting conditions which yields in FNi+1 and Ff i+1 . The mean normal stress σc and shear stress τc acting at the interface having length (li+1 − li ) were calculated as σi =

FNi+1 − FNi dw (li+1 − li )

(3.5)

τi =

Ff i+1 − Ff i dw (li+1 − li )

(3.6)

Conducting his experiments using the above-described technique, Loladze [52] found that the distributions of the normal and shear stresses correspond qualitatively to those found by Andreev (curve 1, Fig. 3.1(a) and curve 1, Fig. 3.1(b), respectively). The values of the maximum normal stress varied from 900 to 1600 MPa for different steels used in the tests and were strongly related to the yield strength of the work material. In each case, the maximum normal stress near the cutting edge was higher than the yield strength of the work material by a factor greater than two. This maximum stress increases to a small extent with the cutting speed and feed, and decreases as the rake angle increases. Unfortunately, Loladze and subsequent researches did not pay attention to this important experimental finding that resulted from well-prepared and precisely conducted cutting tests.

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Tribology of Metal Cutting

Kato et al. [54] conducted a wide range of cutting experiments using a split tool dynamometer. Their results for different work materials can be qualitatively described by the following curves in Fig. 3.1: • For work hardened and perfectly annealed aluminum, copper and lead–tin alloy, the normal stress distribution corresponds to curve 4 (Fig. 3.1(a)); the shear stress distribution corresponds to curve 3 (Fig. 3.1(b)). Surprisingly, the normal and shear stresses at the plastic part of the tool–chip contact were the same for work hardened and for perfectly annealed aluminum although the full contact and plastic contact lengths were twice greater for the latter. Moreover, the shear stress was found to be 25% higher than the normal stress at the plastic part of the tool–chip contact. • For zinc, the normal and shear stresses closely (qualitatively and quantitatively) follow each other and their distribution corresponds to curve 1 (Fig. 3.1(a)) and curve 6 (Fig. 3.1(b)), respectively. In the author’s opinion, the most important conclusion that can be drawn from these results is as follows. Because the study had only one process variable, namely the work material (all other parameters are kept the same), the state of stress in the deformation zone and thus at the tool–chip interface should be qualitatively the same. Therefore, if metal cutting, as it is believed now [2,34,35,37,55–60], is accomplished by pure (or simple) shearing, the normal and shear (tangential) stress distributions should be the same for all ductile materials. Moreover, the shear and normal stresses should be uniquely related so that the shear stress should not exceed 0.7σ. The experimental results obtained do not support this belief. For example, Barrow et al. [50] used a split tool to obtain the stress distributions while machining a nickel–chromium alloy within a wide range of cutting speeds and feeds. It was found that for some cutting conditions, the peak shear stress was approximately equal to the peak normal stress while the magnitude of this peak was found to depend on the cutting conditions. As argued by Astakhov [36], the triaxial state of stress is the real phenomenon of metal cutting and, since different materials react differently on the degree of triaxiality, they exhibit different strain–stress behavior under the same state of stress. Further researchers [58,61,62] conducted a great number of experimental studies with different work and tool materials in order to determine particular values of maximum normal and shear stress and their distribution along the contact length. Since more sensitive techniques for force measurement became available, the fluctuation of the cutting forces became evident. However, instead of understanding the nature of such fluctuations (as argued above, this fluctuation is a result of cyclical nature of the chip formation process), they just used smoothing or averaging of the experimental forces to obtain steady-state stress distributions [63]. Experimental slipline field method. In order to determine the distribution of the normal and shear stresses at the tool–chip interface, Roth and Oxley [64] analysed an experimental flow field obtained under plain strain conditions using the slipline field technique. According to their perception, a single slipline field which would describe the flow in the two deformation zones in metal cutting (the primary deformation zone which stands for the shear plane and the secondary deformation zone which stands for the

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

133

plastic part of the tool–chip contact) could be constructed using experimental flow field and the measured cutting forces. The following drawbacks of this method are listed as follows: • The cutting speeds used to obtain a specimen to study the experimental slipline field are more than 1000 times lower than those used in the practice of cutting of the same work material. For example, the cutting speed was 0.0125 m/min for free machining steel SAE 1112 in Roth and Oxley experiments [64] while the recommended cutting speed used for the same work material exceeds 300 m/min (Table 21.2 in Ref. [65]). As well-discussed by Zorev [2], there is no similarity between the cutting processes at low cutting speeds (see Chapter 2 “Experimental studies of chip formation and contact processes on the tool face at low cutting speeds” and Chapter 4 “Experimental studies of chip formation and contact processes on the tool face at high cutting speeds” in Zorev’s book [2]). • In order to apply the slipline method, simple shearing was assumed to be the prime mode of deformation in the primary and secondary deformation zones which is obviously not the case in metal cutting [36]. The state of stress in the mentioned deformation zones has not been analysed, hence the z component of the normal stress was ignored. • The method is extremely subjective. For example, the crucially important parameters namely the radius of chip curvature and the tool–chip contact length were a subject of assumptions rather than results of measurements. The normal and shear stress distributions obtained by Roth and Oxley [64] are qualitatively shown in Fig. 3.3(a) by curve 1 and in Fig. 3.3(b) by curve 1. As seen, a stress singularity exists at the point of chip separation from the rake face that cannot be physically justified. Later, Oxley in Chapter 7 “Predictive machining theory based on a chip formation model derived from analyses of experimental flow fields” of his book [35], concluded that “a plastic state of stress exists in the chip over the full contact length and that the deformation in the chip can be represented by a rectangular plastic zone with no sliding at the interface.” (p. 100 in Ref. [35]). Further followers of this method tried to take into account the so-called ploughing force components due to the radius of the cutting edge [38]. After a number of assumptions, the distributions of the normal and shear (tangential) stress were obtained to be uniform over the tool–chip contact length, as shown in Figs. 3.3(a) and (b), curves 2. These results are in direct contradiction with those of previous experimental studies where the division of the contact length into two distinctive parts (plastic and elastic) was clearly observed. Moreover, the singularity of stresses at the point of chip separation from the rake face has never been explained. These distributions of the normal and shear stresses suggest that a constant friction coefficient is the case at the tool–chip interface according to Eq. (3.3). A critical analysis of the above-mentioned and other studies related to stress distribution beyond those analysed above (for example, Refs. [2,34,57,66–69]) shows that it is quite possible that actual stresses and stress distributions may have not yet come to light due to a significant scatter in the results obtained.

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Tribology of Metal Cutting

1 Normal stress

2

(a)

0 0

0.5Ic

Ic

Distance from the cutting edge

Shear stress

2

1

(b)

0 0

0.5Ic

Ic

Distance from the cutting edge

Fig. 3.3. Qualitative representation of the normal (a) and shear (tangential) (b) stress distributions at the tool–chip interface obtained by Roth and Oxley for a free-machining steel (after Astakhov and Outeiro [73]).

3.2.3 Contact stress distribution – modeling Experimental evidences. Multiple experimental studies conducted by Zorev [2], Loladze [52], Poletica [69] and many others conclusively proved that the tool–chip interface consists of plastic and elastic parts. Figure 3.4 shows that the plastic part of the tool–chip interface can be clearly observed on the tool rake face. Therefore, the uniform stress distribution shown in Fig. 3.3 is in direct contradiction with the known experimental observations. Zorev [2] studied the length of the plastic part using a quick-stop device and conclusively proved that the whole contact length lc is divided into two distinctive parts: the plastic part, lc−p which extends from the cutting edge and the elastic part lc−e , from the plastic part to the point of tool–chip separation. Zorev showed that the contact length, lc is a function of the cutting speed, as shown in Fig. 3.5. Similar experimental results were obtained by Poletica [69]. Summarizing the results of multiple experiments,

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

135

Fig. 3.4. The tool–chip interface consists of two parts, namely plastic and elastic.

lc, lc−p (mm) 2.0 lc 1.5

1.0 lc−p 0.5

30

60

90

120

150

n (m/min)

Fig. 3.5. Influence of cutting speed (ν) on the tool–chip contact length (lc ) and on the plastic part lc−p of the tool–chip contact length. Orthogonal cutting, work material – steel 4130, rake angle γ = 5◦ and uncut chip thickness t1 = 0.15 mm.

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Tribology of Metal Cutting

Abuladze [70] proposed the following expression to calculate the length of the plastic part of the tool–chip interface lc−p = t1 [ζ (1 − tan γ) + sec γ]

(3.7)

Model and FEM analysis. The contact problem at the tool–chip interface can be modeled as the contact of two bodies made of dissimilar materials. As such, one body deforms elastically within the contact interface (the tool), and the other body (the chip) contains elastic and plastic regions within this interface. Moreover, there is relative sliding between these two contacting bodies and thus the traction develops over the contact length. In the considered case of the tool–chip contact, it is not simple to determine the exact contours of the deformed surfaces and other boundary conditions so that the exact solution of the stated contact problem is rather difficult. Therefore, simplifications have to be introduced to develop a suitable model. All real contacts, like all real engineering components, are three-dimensional, and therefore theoretically demand a solution in the three-dimensional theory of elasticity of elastoplasticity [71]. However, there are some simple cases where it is feasible to approximate the geometry to one or two dimensions. As discussed in Chapter 1, orthogonal cutting is always considered as a two-dimensional problem. Thus, in order to investigate the tool–chip contact problem, plane contact problems will be considered, i.e. those where it is assumed that displacements are restricted to a single plane, the xy plane. Among the two-dimensional contact problems known, those where the contacting bodies are considered to be half-planes, i.e. semi-infinite bodies with remote boundaries are looked at, provided that the width of the resulting contact is negligible in comparison with the bodies’ radii of curvature. Contacts where this is so are said to be non-conformal [71]. A wide range of non-conformal contact problems may be readily solved in two stages. First, the mixed boundary value problem (where displacements are specified within the contact, and the remainder of the free surface is free of tractions) is reduced to an elasticity problem of the first kind, i.e. where the tractions are specified everywhere. Second, the interior stress field due to these tractions is found by applying the Muskhelishvili potential [72]. Figure 3.6 shows the general class of contact problems. Subscripts 1 and 2 will be added to the elastic constant relating to the upper and lower bodies respectively and a mathematical sign conversion is adopted for the tractions, i.e. direct tractions (contact stresses) ps (x) are positive tensile and shear tractions qs (x) are positive when acting to the right on the lower body. According to the known results [71], the equations for displacements υs1 and υs2 are ∂υs1 κs1 + 1 = ∂x 4G1 π ∂υs2 κs2 + 1 = ∂x 4G2 π

 

κs1 + 1 ps (ς) dς − qs (x) x−ς 4G1

(3.8)

ps (ς) dς κs2 + 1 − qs (x) x−ς 4G2

(3.9)

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

Body 1

137

hs(x)

(a)

Cs Body 2 x y

Ps

Body 1

(b) Qs

x

Body 2

Fig. 3.6. Contact of two bodies: (a) in the undeformed state where they can freely interpenetrate each other and (b) in the loaded state with no interpenetration permitted.

where κs = (3 − νs )/(1 + νs )

in plane stress

(3.10)

κs = 3 − 4νs

in plane strain

(3.11)

νs is the Poisson’s ratio, G is the modulus of rigidity (shear modulus), qs (x) = µf ps (x), where µf is the friction coefficient. In general, as two bodies are pressed together, deformation must occur so that the deformed bodies will conform within the contact. If the unloaded state of the bodies could freely interpenetrate each other, so that the amount of overlap given by hs (x) with maximum cs (Fig. 3.6(a)) within the contact patch, the relative y direction displacements of surface points υs1 − υs2 must be equal to the degree of surface overlap, so from Eqs. (3.8) and (3.9) the required displacement is [71] 1 1 ∂hs (x) = As ∂x π



ps (ς) dς − βs qs (x) , x−ς

(3.12)

where κs1 + 1 κs2 + 1 + 4G1 4G2

(3.13)

Γ (κs1 − 1) − (κs2 − 1) Γ (κs1 + 1) + (κs2 + 1)

(3.14)

As = and βs =

138

Tribology of Metal Cutting G2 G1

Γ =

(3.15)

Thus, As is the measure of the compliance of the bodies, while βs , sometimes referred to as the Dundrus’ constant [71], is a measure of the elastic mismatch of the materials. When the solution to problems under plane strain conditions is needed, then As and βs become   2 2 1 − νs1 1 − νs2 1 − νs1 1 − νs2 As = (3.16) + ≡2 + G1 G2 E1 E2 βs = =

(1 − 2νs1 )/2G1 − (1 − 2νs2 )/2G2 (1 − νs1 )/G1 + (1 − νs2 )/G2 1 [(1 + νs1 ) (1 − 2νs1 )]/E1 − [(1 + νs2 ) (1 − 2νs2 )]/E2     2 /E + 1 − ν2 /E 2 1 − νs1 1 2 s2

(3.17)

As known from Ref. [71], the elastic constants of the contacting bodies enter the problem only through the composite parameters As and βs . Thus, all pairs of materials yielding the same values of As and βs will have the same solution to the contact problem. In metal cutting, one (the tool) of the two contact bodies is rigid so the elastic constant of the other body (the chip, when considering the tool flank–workpiece interface) are adjusted appropriately. As such As =

2 1 − νs2 1 − νs2 ≡2 G2 E2

(3.18)

1 − 2νs2 2 (1 − νs2 )

(3.19)

βs =

As shown by Hills [71], if the relative tangential displacement of any pair of surface points is hs−t (x) (Fig. 3.6(a)), then this displacement is 1 ∂hs−t (x) 1 = As ∂x π



qs (ς) dς − βs ps (x) x−ς

(3.20)

It is understood that integrations in Eqs. (3.12) and (3.20) are carried out over the entire contact zone. Thus, to assure equilibrium with external forces Ps and Qs , the following should be kept in mind  Ps = − p (ς)dς

(3.21)

 Qs = where Ps is a positive compressive force.

q (ς)dς,

(3.22)

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

Ps

Ps

rs

(a)

hs

139

(c)

x as

x as1

as1

as

p

p Elastic limit p(x) p(x)

(b)

(d)

x

x

Fig. 3.7. Indentation of a half-plane by: (a) a rigid flat-ended punch and (b) contact stress distribution, (c) a rigid round-ended punch and (d) contact stress distribution (after Astakhov and Outeiro [73]).

Poletica [69] was the first researcher who attempted to model the tool–chip contact problem by analyzing the representation of the tool–chip interface as a rigid, flat-ended axisymmetric cylindrical punch that is pressed into a viscoelastic material, which can be regarded as semi-infinite, that is, a half-space as shown in Fig. 3.7(a). The contact patch is of fixed size, independent of the applied load and determined solely by the width of the indenter. Since the displacement of the half-plane, hs = constant and no relative motion is allowed, Eq. (3.12) in normalized coordinates (x = as s, ς = as r) gives

1 π

as −as

1 ps (ς)dς = x−ς π

+1 −1

ps (r)dr =0 s−r

(3.23)

and its inversion as in Ref. [71] is C p(s) = √ 1 − s2

or

p(x) = 

C 1 − (x/as )2

(3.24)

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Tribology of Metal Cutting

In Eq. (3.24), C, the constant term included as pressure, is singular at each end of the contact interval. This constant can be found using Eq. (3.21) as as Ps = p(x)dx

(3.25)

−as

which gives p (x) =



Ps

as π 1 − (x/as )2

(3.26)

This is known as the Boussinesq solution [71]. Figure 3.7(b) shows the contact pressure distribution, p(x) calculated using Eq. (3.26). The contact pressure is singular at the edges of the contact. In reality, the contact pressure is limited by the elastic limit of the body 2 (the chip), as shown in Fig. 3.7(b). Besides, the edges of the punch (the tool) are not perfectly sharp. If the sliding of the punch is allowed so that all points within the contact are slipping in the same direction, then the shear stress acts over this contact. When the friction coefficient, µf is constant, this shear stress is defined as |q(x)| = µf p(x)

(3.27)

so that As π

as −as

ps (ς)dς + As βs µf p(x) = 0 x−ς

(3.28)

In reality, however, the punch does not have sharp edges as those shown in Fig.3.7(a). Moreover, its face is not ideally flat. Therefore, the problem of indentation by a general, convex body should be considered next to approach reality. Figure 3.7(c) shows the rigid punch having a spherical face of radius rs , which is pressed into a viscoelastic material that can be regarded as semi-infinite, i.e. a half-space. If the contact is sufficiently small in comparison with the face radius rs , then the problem of contact stress distribution has a direct solution [72]. The distribution of the contact stress for this case is shown in Fig. 3.7(d). As seen, when x = ±as1 , the contact pressure becomes zero, and when x = 0, this pressure is maximum. The next step is to start building a model which is closer to the real conditions of the tool–chip interface. Figure 3.8 shows the following essential features of this interface: • The resultant cutting force R does not intersect the middle point of the tool–chip contact length OB. Rather, the line of its action is shifted toward the tool point O, which represents the projection of the cutting edge.

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

141

E Chip

Tool g

B R

D A

wac C

O Workpiece

Fig. 3.8. Some characteristic points at the tool–chip interface (after Astakhov and Outeiro [73]).

• The resultant cutting force R is not applied perpendicular to the tool rake face having the rake angle γ. Rather, it acts at the so-called angle of action, ωac relative to the direction of tool–workpiece relative motion [2]. As a result, the normal and shear stresses act over the tool–chip interface. • As a result of asymmetrical application of the cutting force, the contact pressure (stress) distribution is no more symmetrical as in the above-considered case. • There is relative sliding between the tool and the chip so that the friction force should be considered in the analysis of the contact stresses at the tool–chip interface. Considering Fig. 3.8, one can conclude that the tool point O represents the sharp edge of the punch. According to Figs. 3.7(a) and (b), a normal stress singularity should be the case in this point. In reality, however, two factors hamper such a singularity. First, the cutting edge is never perfectly sharp and thus the intersection of the rake and the flank surfaces of the cutting insert is not a line but rather a surface of finite radius (this issue will be discussed later in this chapter). Second, as discussed in Chapter 1, a zone of plastic deformation in the workpiece forms in the vicinity of this point and a crack originates from the tool point O in each cycle of chip formation. As known from Ref. [36], plastic deformation and cracks are means of stress relaxation, so the discussed stress singularity never occurs in reality. Continue to refer to Fig. 3.8, one can see that the other side of the tool–chip contact (point B) resembles edge points shown in Fig. 3.7(c), i.e. the contact pressure becomes zero at this point. Figure 3.9(a) shows a model of indentation with a flat-face punch and asymmetrical loading of the punch by force Ps applied at point D. As seen, the line of action of force Ps does not pass through the middle point of the contact length (the xy coordinate origin). Points O, D and B corresponds to those shown in Fig. 3.8. The asymmetric application of Ps results in asymmetric deformation, as shown in Fig. 3.9(b).

142

Tribology of Metal Cutting y

Ps

O1

B

D

Ps

(a)

B

O

D

(b)

O

x

x

as

as

ζp

as

y

as

Ms

Ms Ps

Ps

(c)

E

O

O1

E

(d)

O

B

x

x as

as

zp as1

as

Fig. 3.9. Indentation of a half-plane by asymmetrically-loaded punch: (a) original model unreformed and (b) deformed configurations; (c) modified model undeformed and (d) deformed configurations (after Astakhov and Outeiro [73]).

The contact stress distribution for the considered case was studied by Muskhelishvili [72], who obtained the following exact solution p(x) =

π



Ps as2

− x2

−

4G2 cs x ,  (κs + 1) as2 − x2

(3.29)

where cs is cs =

Ms (κs − 1) 2πG2 as2

(3.30)

If the sliding of the punch is allowed so that all points within the contact are slipping in the same direction and when the friction coefficient, µf is constant, the stress distribution

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

143

becomes p(x) =

cos πρs Ps (κs + 1) − 8πG2 cs ρs as − 4πG2 cs x , 1 1 π (κs + 1) (a − x) 2 +ρs (a − x) 2 −ρs s

(3.31)

s

where ρs =

κs − 1 1 arctan µf π κs + 1

(3.32)

It follows from Eqs. (3.29) and (3.31) that when x = ±as , the contact pressure p(x) = ∞ as in Eq. (3.26). However, the distributions given by Eqs. (3.29) and (3.31) are characterized by significant asymmetry as seen from Fig. 3.10(a) [73]. This figure shows that when the sliding with friction is allowed, the contact stress, p(x), is no more singular at the punch rear edge, but it tends to zero. Moreover, the accounting for friction (allowing the sliding at the tool–chip interface) does not affect this distribution significantly. The further development of this model is shown in Fig. 3.9(c) where the force is shifted to the center of the punch and thus the moment Ms is applied to compensate for this shift. As such, this moment causes the angular punch displacement characterized by angle ζp and the force Ps causes the displacement of the punch in the y direction (the vertical displacement), as shown in Fig. 3.9(d). As seen, this model is obtained assuming that the moment Ms is great enough such that the point E is not in contact with the workpiece and the contact length is no more axisymmetrical. Rather, it may be thought of as consisting of two parts, as1 and as , as shown in Fig. 3.9(d). Studying such a contact problem, Galin [74] obtained the following analytical solution for the contact stress distribution.  2Ps x + as1 p(x) = (3.33) π (as + as1 ) as − x

(a)

(b)

Fig. 3.10. Contact stress distribution (p(x)) produced by applying asymmetrical loading over the punch: (a) original model sliding with friction is allowed and not allowed, (b) modified model with an asymmetrical contact length for the original model. (Conditions: as = 1 × 10−3 m, Ps = 0.5 N, µf = 0.5, Es2 = 210 GPa, νs2 = 0.3) (after Astakhov and Outeiro [73]).

144

Tribology of Metal Cutting

As seen, if x = −as1 then p (x) = 0 and if x = as then p (x) = ∞. Equation (3.33) does not include Ms directly. This moment is accounted for by as1 , which is a function of Ms . Figure 3.10(b) [73] shows the contact stress distribution, p (x), produced in the case of an asymmetrical contact length. This distribution is similar to the case of full symmetrical contact with sliding, as shown in Fig. 3.10(a). However, in the case of the asymmetrical contact length, the stress at point B (Fig. 3.9(d)) is zero. Although the above-discussed model provides some insight on the contact stress distribution, it is obviously still far from reality because the chip can hardly be modeled by the half plane representation used in the model. To improve the model, a 3D problem of contact of a rigid profile with elastic strip should be considered as the next logical step in model development [69]. Figure 3.11 shows such a model. Using a general form of solution obtained by Muskhelishvili [72] as applied to the considered case, one can obtain the following expression for the contact stress distribution 2N p(x) = πdw1 lc



lc − x x

(3.34)

where lc is the contact length, dw1 is the chip width. More accurate results can be obtained if friction over the contact length is considered. As such, the boundary conditions for the stress and displacement should be as follows: if x < 0 or x ≥ lc then p(x) = σc = 0 and τc = 0. As such 2N p(x) = πdw lc (1 − 2ρs )



lc − x x

1 −ρs 2

(3.35)

,

Workpiece

y

A

Chip lc

lc /2

lc / 2

g O

D

O1 R

N

B

E

x

Tool

F

Fig. 3.11. Contact length and its parts (after Astakhov and Outeiro [73]).

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

145

where ρs calculates using Eq. (2.66). As seen, when µf = 0, ρs = 0 and Eq. (3.35) becomes equivalent to Eq. (3.34). For convenience, the stress at the tool–chip interface can be represented as the product of two factors p(x) = qN p1 (x),

(3.36)

where the first one, qN =

N dw l c

(3.37)

is the mean contact stress at the tool–chip interface, and the second one is a dimensionless function 2 cos πρs p1 (x) = π (1 − 2ρs )



lc − x x

1 −ρs 2

(3.38)

characterizing the distribution law of the normal pressure over this interface. Equation (3.38) can be modified further if a new variable ψs = x/lc is introduced. As such 2 cos πρs p1 (ψs ) = π (1 − 2ρs )



1 − ψs ψs

1 −ρs 2

(3.39)

Figure 3.12 shows the distribution of the contact pressure, p1 (ψs ) obtained under different friction coefficients [73]. This figure shows that accounting for friction (allowing the sliding at the tool–chip interface) does not affect this distribution significantly. One problem about the exact location of the point of application of the penetration force on the tool rake face remains unsolved. To resolve this problem, an FEM model for the case shown in Fig. 3.11 was developed using ANSYS commercial FEA software [73]. The developed FEM model utilized the work material properties (E, ν), the tool geometry (γ) and the results obtained from orthogonal cutting tests (forces, N and F , the final angle of the surface of the maximum combined stress (known as the shear angle), and the tool–chip contact length, lc ). The results for the tool–chip contact stress distribution and equivalent stress distributions in the workpiece and in chip are shown in Figs. 3.13(a) and (b) for the following conditions: E = 196 GPa, νs = 0.26, N = 1550 N, F = 1215 N, γ = 0◦ , lc = 0.712 mm, l1 = 0.284lc . As seen, the maximum stress is found to be at the region of the cutting edge. This stress decreases exponentially towards the point of chip separation where this stress is zero. Interface stress distributions based on the system model. Based upon the system approach in metal cutting [36,75], this section aims to explain the nature of a significant

146

Tribology of Metal Cutting

Fig. 3.12. Contact stress distribution (p1 (ψs )) produced by applying asymmetrical loading over the punch and considering an asymmetrical contact length, for different friction coefficients (Conditions: as = 1 × 10−3 m, as1 = 5 × 10−4 m, Ps = FN = 0.5 N, µf ∈ [0, 3], Es2 = 210 GPa and νs2 = 0.3) (after Astakhov and Outeiro [73]).

scatter in the reported stress distributions at the tool–chip interface by studying the dynamics of stress formation and distribution at this interface. Finite element simulation makes it possible to establish the distributions of the normal and shear stress at the tool–chip interface, as well as the dynamics of these distributions within a chip formation cycle. It is instructive to trace the above-mentioned distributions by applying FEM analysis with incremental loading. The detailed procedure of such a simulation is developed by Astakhov [36]. Some relevant results obtained are now considered. The shear stress distribution at the beginning of each new chip formation cycle is shown in Fig. 3.14. As seen, this distribution within the tool–chip interface has two distinctive regions. In the first region, the shear stress distributes uniformly and increases with the applied load. Furthermore, both the length of this region and the stress magnitude do not change with the rake angle. In contrast, in the second region, the shear stress decreases at a rate that is a function of the rake angle. A comparison of the results shown in Fig. 3.14 with the known results shown in Fig. 3.1(b) shows that there is no contradiction in the reported results. In other words, all the reported shear stress distributions (curves 1 to 6 in Fig. 3.1(b)) at the tool–chip interface may occur as being considered at different instants over a chip formation cycle and under different cutting conditions.

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

147

1.E+07

p (ys )

8.E+06

6.E+06

4.E+06

2.E+06

0.E+00 0.0

0.2

0.4

0.6

0.8

1.0

ys

(a)

(b) Fig. 3.13. Example of the FEM analysis: (a) tool–chip contact stress distribution and (b) von Mises stress distributions (A = 0.40; C = 1.99; E = 3.58; G = 5.17 . . . O = 11.5; P = 12.3; σ max = 12.7 MPa) in the workpiece and chip (after Astakhov and Outeiro [73]).

Astakhov [36] compared the evolution of shear stress during the cut-in period with that of stabilized cutting and showed that the shear stresses at the tool–chip interface are almost 30% higher during cut-in period than that in stabilized cutting to achieve the same effect (for example, to form the stress level corresponding to the beginning of failure of the work material). This is the prime cause for the reduction of tool life in interrupted cutting. Figure 3.14(b) shows the evolution of the normal stress up to the beginning of each chip formation cycle. As seen, the presence of a partially formed chip affects the normal

Shear stress (GPa)

148

Tribology of Metal Cutting

0.8

5

0.8 5 4

Rake angle −18°

Rake angle 0°

4

0.4

0.4 3

2

2 1

0 0

0.27

0.54

3

1

0

0.81 1.08 0 0.27 Distance from the cutting edge (mm)

0.54

0.81

1.08

(a) 2.0

Rake angle −18°

Rake angle 0°

Rake angle +18°

Normal stress (GPa)

1.6

4

5

4

5

4

5

1.2 3

3

3

0.8 2

2

2

0.4 1

1

1

0 0

0.27

0.54

0.81

0

0.27

0.54

0.81

0

0.27

0.54

0.81

Distance from the cutting edge (mm)

(b)

Fig. 3.14. Dynamics shear (tangential) (a) and normal (b) stress distributions at the beginning of a new chip formation cycle. Curves 1 to 5 correspond to increasing load with the increment of 250 N, respectively. Work material – AISI 1045 steel, tool material – P20.

stress distribution. The maximum normal stress becomes higher when increasing the rake angle. Moreover, the location of this maximum shifts towards the cutting edge. As with the shear stress, a comparison of the results shown in Fig. 3.14(b) with the known results shown in Fig. 3.1(a) shows that there is no contradiction in the reported results. In other words, all the reported normal stress distributions (curves 1 to 6 in Fig. 3.1(a)) at the tool–chip interface may occur as being considered at different instants over a chip formation cycle and under different cutting conditions. The above analysis of the normal and shear stress distributions at the tool–chip interface results in two important conclusions: • Increasing the rake angle leads to the reduction in the contact length that results in an increase in the maximum shear and normal stresses at this interface. Moreover, the maximum of the normal stress shifts towards the cutting edge. Because the use of high positive tool geometry (which stands for high rake angles) has become a new tendency recently introduced and followed widely by the leading tool producers, the transfer rupture stress of tool materials for such applications should be increased.

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

149

• The fluctuations of the normal and shear stresses at high frequencies [36] explain the high scatter in the results of using different coatings. Obviously, these fluctuations should be accounted for in the design of any particular coating.

3.2.4 Experimental study The basic tribological characteristics of the cutting process determine not only tool wear or contact temperature but also other physical characteristics of this process. These tribological characteristics cannot be considered apart from other parameters of the metal cutting process as they affect these parameters directly. It is very important to establish the prime and dependent parameters as well as their correlations in order to control the cutting process. The following considerations are based on the excellent experimental results obtained by two prominent researchers in the field of metal cutting tribology, namely Poletica [76] and Zorev [2]. In the author’s opinion, these results have never been properly presented, understood and appreciated. As a result, they were never used for further developments in the design and optimization of metal cutting processes and cutting tools although the potential of these findings is tremendous. Methodology. In the tests, the contact length was measured on the actual cutting insert under a microscope. To verify the accuracy of such a measurement, the cutting insert before the actual testing was plated with a thin copper layer by dipping it in copper sulfate solution. The comparison of the obtained results showed no noticeable difference between the results obtained using these two methods of contact length determination. In special cases, however, when the tests were conducted using soft work materials and thus, there were no clearly visible wear marks on the tool rake face, a thin layer of a neutral water-based paint was used to determine the contact length accurately. The average integral contact temperature was measured using the tool–work thermocouple technique. Its principle is discussed later in this chapter. The calibration of such a thermocouple is discussed in Ref. [36,68]. Other characteristics were obtained through the measurements of the cutting force components [36]. Contact length. As discussed above, the tool–chip contact length known as the length of the tool–chip interface determines major tribological conditions at this interface as temperatures, stresses, tool wear, etc. This length is found to be very sensitive to any change in the parameters and characteristics of the cutting process. Therefore, it is of great interest to find out the correlations between these characteristics and the contact length because the optimization of tribological processes at the tool–chip interface can be accomplished only when these correlations are known and well understood. Figure 3.15(a) shows the correlation between contact length and the uncut chip thickness for different work materials. As seen, the contact length increases with the uncut chip thickness for all materials tested although at different rates. This rate is much greater for soft (HB47) copper having high thermal conductivity than for relatively hard (HB190) titanium alloy having low thermal conductivity.

150

Tribology of Metal Cutting Ic(mm)

Ic(mm) 1

3

2 1

3 3

2 3

2

2 4

4

1

5

1

6

0

0.2

0.4

(a)

t1(mm)

0

0.2

0.4

t1(mm)

(b)

Fig. 3.15. Correlation between the contact length and the uncut chip thickness: (a) for different work materials: 1 – copper, 2 – lead, 3 – aluminum 2014, 4 – steel AISI E9310, 5 – cadmium and 6 – titanium Grade 1, (b) for different work materials under constant ζ: 1 – copper (ζ = 10), 2 – steel AISI E9310 (ζ = 3.2), 3 – beryllium copper UNSC17000, HB110 (ζ = 4) and 4 – tool steel O7 (ζ = 2.45).

Analyzing the correlations shown in Fig. 3.15(a), one should keep in mind that the uncut chip thickness directly affects the chip compression ratio (CCR) which also affects the contact length. Therefore, it is of interest to separate the influence of these two characteristics on the contact length. Figure 3.15(b) shows the influence of uncut chip thickness on the contact length under invariable CCR (ζ = Const). As follows from this figure, the contact length is directly proportional to the uncut chip thickness for different work materials. Although Fig. 3.15(b) shows only correlations for four work materials, this rule was proven to be true for a wide variety of work materials. Therefore, the uncut chip thickness can be regarded as an independent parameter of the cutting process that directly affects the contact length. The contact length decreases with the cutting speed for different work materials as follows from the data illustrated in Fig. 3.16. As seen, steep dependences hold for relatively low cutting speeds while the contact length shows a little dependence on the cutting speed in the range of normal and high cutting speeds. This can be attributed to the corresponding change in the average contact temperature at the tool–chip interface, which changes significantly with the cutting speed for low cutting speeds and then this change slows down when the cutting speed increases further. Therefore, the dependences shown in Fig. 3.16 reflect the result of mutual action of the cutting speed and temperature (the temperature–speed factor as termed by Zorev [2]). Figure 3.17 shows that the same tendency holds for a wide variety of steels. As seen, the contact length also reduces with the hardness (the carbon content) of the steel. The scatter in experimental results is

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

151

lc(mm) 6 5 2

4

3 1 2 1 0

80

160

240

n(mm/min)

Fig. 3.16. Correlation between the contact length and the cutting speed for different work materials: 1 – titanium Grade 1, 2 – beryllium copper UNSC17000, HB200, 3 – beryllium copper UNSC17000, HB110, 4 – Armco iron, 5 – copper and 6 – aluminum 2014.

lc(mm)

3.0 1 2.0 2 3

4 1.0

5 0 0

40

80

120

160

200

240

n (mm/min)

Fig. 3.17. Correlation between the contact length and the cutting speed for different steels: 1 – AISI 1010 (0.1% C), 2 – AISI1020 (0.2% C), 3 – AISI 1060 (0.6% C), 4 – AISI 1080 (0.8% C), 5 – AISI 07 (1.2% C). Normal rake angle γn = 10◦ , depth of cut dw = 4 mm and cutting feed f = 0.156 mm/rev.

152

Tribology of Metal Cutting

1.8

Ic (mm) 3

2 1.0

1

0.2 −40

−20

0

20

40

gn(°)

Fig. 3.18. Influence of rake angle on the contact length: 1 – cadmium, 2 – steel AISI E9310 (t1 = 0.16 mm, ν = 22 m/min), 3 – steel AISI E9310 (t1 = 0.28 mm, ζ = constant = 2.5).

much smaller for harder steels. Analysis of Figs. 3.16 and 3.17, however, shows that the dependence of the contact length on the cutting speed directly resembles the dependence of CCR on the cutting speed (Fig. 2.5 and Ref. [77]). Figure 3.18 shows the influence of normal rake angle on the contact length for different work materials. As seen, the contact length decreases with the rake angle. Moreover, this conclusion is true even when the CCR is kept invariable. Therefore, the rake angle affects the contact length in two ways, namely, directly and through CCR. One should notice, however, that the influence of rake angle on the contact length is not significant. As follows from the foregoing considerations, among the three considered factors (the uncut chip thickness, cutting speed and rake angle), only the uncut chip thickness affects the contact length directly. The other two factors affect the contact length through CCR. This allows to introduce a similarity criterion to be used in metal cutting tribology, namely the Poletica criterion (Po-criterion) Po =

lc t1

(3.40)

The Po-criterion, strongly depends on CCR and weakly depends on the rake angle as follows from the experimental data presented in Fig. 3.19(a). As seen, the influence of rake angle is within the normal experimental scatter. Moreover, it was found that the Po-criterion remains invariant to changes in the mechanical and physical properties of the work material. As can be seen in Fig. 3.19(b), the hardness of the work material does not affect the dependence of Po-criterion on CCR. Considering this test, one should note that beryllium copper is an excellent test material because its mechanical properties

Tribology of the Tool–Chip and Tool–Workpiece Interfaces Po

153

Po

10

8

8 6 6 4 4 g = −10° g = 0° g = 10° g = 20°

2 0

1

2

4

3

5

f = 0.07 0.15 0.26 0.34 (mm/rev) HB110 HB200 HB320

2

z

0

1

2

(a)

3

4

5

6

z

(b)

Fig. 3.19. Influence of chip compression ratio on Po-criterion: (a) in machining steel AISI E9310, tool material P20 (79% WC, 15% TiC, 6% Co), cutting feed f = 0.07 − 0.43 mm/rev and cutting edge angle κr = 70◦ ; (b) in machining beryllium copper UNSC17000 of different hardnesses. Tool material – HSS M30 (92% WC, 8% Co).

can be changed in a wide range by heat treatment while the phase composition and microstructural parameters remain practically unchanged. Figure 3.20 presents the results of cutting tests with various work and tool materials having a wide range of physical and mechanical properties. In this figure, the normalized chip compression ratio, ζt is used instead of ζ. It is calculated as ζt =

ζ , dw1 /dw

(3.41)

where dw1 is the chip width. This is done to include into consideration the results of the cutting test with copper and Armco iron. When cutting these two materials, the chip width changes considerably compared to the width of cut (the depth of cut), whereas for many other work materials, the ratio dw1 /dw ≈ 1 if measured properly [36]. Although some scatter of experimental results can be observed in Fig. 3.20, it can be concluded that a single-valued functional relationship Po = f (ζt ) exists within a wide variety of cutting parameters. Statistical evaluation of the obtained experimental results allows obtaining the following relationship for the Po-criterion Po =

lc = ζtkt , t1

where kt = 1.5 when ζt < 4, and kt = 1.3 when ζt ≥ 4.

(3.42)

154

Tribology of Metal Cutting Po Copper, UNSC17000 cutter, g = 25° Copper, Ti Grade 1 cutter, g = 25° Steel O7, annealed, g = 10° Copper, HSS M35 cutter, g = 10° Beryllium copper, HB110, g = 10° Beryllium copper, HB200, g = 10° Beryllium copper, HB320, g = 10° Armco iron, g = 10°

40

30

20

10

Steel E9310,M30 cutter, g = −10°, 0°, 10°, 20°

0 1

5

9

13

17

zt

Fig. 3.20. Influence of chip compression ratio on Po-criterion in machining various work materials using different tool materials and tool rake angles.

The correlation between the Po-criterion and CCR obtained experimentally and expressed by Eq. (3.42) represents the condition of static equilibrium of the chip. Figure 3.21(a) shows the simplified model of chip formation at the last phase of a chip formation cycle for the cutting tool with the full rake face. In this picture, ϕ is the angle of final inclination of the surface of maximum combined stress approximated by a plane, point B is the coordinate of application of normal force N (which can be thought of as the coordinate of the center of gravity of the distribution of the normal stress along the tool– chip contact), point D is the coordinate of application of normal force Fn on the surface of maximum combined stress approximated by a plane, OC = lc is the contact length. Let us introduce the dimensionless coordinates of points B and D as follows: ψB =

OB lB = OC lc

(3.43)

ψD =

lD sin ϕ OD = OA t1

(3.44)

Because the chip is in static equilibrium, the sum of the moments of the normal forces is zero, i.e. Po =

lc Fn ψD = t1 N ψB sin ϕ

(3.45)

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

155 gn1

gn C

lc A t1

j Fs

R

B

lB lD

R

B

g wac

A

F N

t1

D

j

O

Fn

lrr

O

(a)

(b)

Fig. 3.21. Simplified model of chip formation at the last phase of a chip formation cycle: (a) for the cutting tool with the full rake face and (b) with the restricted length rake face.

Normal forces N and Fn can also be expressed through the resultant force R using the angle of action, ωac (Fig. 3.21(a)) as N = R sin (ωac + γ)

(3.46)

Fn = R sin (ωac + ϕ)

(3.47)

Substituting Eqs. (3.46) and (3.47) into Eq. (3.45), one can obtain   ψD 1 + tan ωac tan−1 ϕ lc = Po = t1 ψB (cos γ − sin γ tan ωac )

(3.48)

Dimensionless coordinate ψB is defined by the shape of distribution of the normal stress because the location of point B is determined by the position of the center of gravity of the distribution area. As proven by Zorev [2], the shape of this distribution curve is stable depending weakly on the process parameters. It means that ψB varies within very narrow range so, to the first approximation, it can be accepted that ψB = constant. Then, it follows that ψD = constant. Using these approximations (which, in fact, quite accurately resemble the reality of the cutting process), one can represent Eq. (3.48) as Po =

lc = f (ϕ, ωac ) t1

(3.49)

i.e. the Po-criterion is a function of two angles, namely ϕ and ωac . Zorev showed [2] that, for a given work material, ϕ and ωac are directly correlated. As such, the Po-criterion is a function of only one angle, say ϕ. It follows from the

156

Tribology of Metal Cutting

model shown in Fig. 3.21(a) that ϕ = arctan

cos γ ζ − sin γ

(3.50)


where, by definition, CCR ζ = t2 t1 . It directly follows from Eq. (3.50) that ϕ depends on CCR, ζ, and on the rake angle, γ. However, the influence of γ is not significant as follows from the structure of Eq. (3.50). Therefore, it can be written with reasonable accuracy Po =

lc = f1 (ζ) t1

(3.51)

The same conclusion follows from the above-discussed experimental results represented by Eq. (3.42). Although the obtained result is known for years, it has never been explained. In the author’s opinion, a possible explanation is rather simple as it directly follows from the generalized model of chip formation discussed in Chapter 1. Because cracks form at points A and O (Fig. 3.21(a)) due to the combined action of compressive and bending stresses, the maximum combined stress at these points forms due to compressive force and bending moment imposed by the force resultant R. As such, the compressive force is determined by the tool–chip contact area while the bending moment is determined by both the contact area and the distance lB . When the cutting parameters (primarily the properties of the work material) are changed so that CCR increases, a much higher contact area and lB are needed to achieve the same critical combined stress at points A and O because the cross-sectional area of the partially formed chip–cantilever increases with CCR. This explanation can be easily verified experimentally using tools with restricted contact length. When the tool rake face is straight, the contact length lc sets itself to the value required by the static equilibrium condition (Eq. (3.48)). This contact length is termed as the natural contact length. If the length of the rake face is made smaller than the natural contact length, then the resultant contact length known as restricted contact length, lrr is as shown in Fig. 3.21(b). As shown in this figure, the restricted rake face is made with the normal rake angle, γn while the secondary rake face is made with γn1 . It is understood that according to the explanation provided, if the contact length (the contact area in reality) decreases, the contact stress must increase to provide the same combined stress at points A and O. When a tool with restricted contact length is used, the equilibrium condition set by Eqs. (3.48) and (3.49) should be justified with this new contact length. However, this length is no more a function of ϕ and ωac but rather becomes an independently controlled parameter. Some representative experimental results are shown in Fig. 3.22. As seen, the reduction of the contact length leads to the corresponding increase in the contact stress as was predicted above. Moreover, this increase exactly corresponds to an increase in the compressive force and bending moment needed to keep the critical combined stresses

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

157 qc−r (°C)

sc(MPa) Mean contact temperature

800

650

600

600 Specific normal contact stress

400

550

200

500 1

2

3

lc (mm)

Fig. 3.22. Influence of contact length on the specific normal contact stress and mean contact temperature at the tool–chip interface. Work material AISI steel 1020, tool material P20 (79% WC, 15% TiC, 6% Co), normal rake angle γn = 20◦ , depth of cut dw = 4 mm, cutting feed f = 0.55 mm/rev and cutting speed ν = 60 m/min.

at points A and O. The results of a great number of tests conducted by Zorev [2] and Klushin [78] with various work materials under a wide range of cutting conditions conclusively proved this point. Another important conclusion follows from Fig. 3.22: the mean contact temperature at the tool–chip interface decreases while the specific normal stress at this interface increases. This is in direct contradiction with the known results of friction test where the temperature increases with the contact stress (for example, see Ref. [79]). It is, however, in perfect agreement with the above-discussed model of energy distribution in metal cutting according to which high temperatures in metal cutting are due to contact processes at the tool–chip and tool–flank interfaces and not due to plastic deformation in the deformation zone. One more time, the obtained result signifies the importance of understanding the metal cutting tribology. Contact stresses. Multiple experimental data obtained by Zorev [2] and Poletica [69] conclusively proved that the shapes of the normal and shear stress distributions remain the same under wide variations of cutting conditions, tool and work materials properties and other parameters and factors of the cutting process. Therefore, it is reasonable to consider the mean value of these stresses which characterize tribological conditions at the tool–chip interface. The obtained data also show that the mean shear stress, τc is the most stable characteristic of cutting tribology. Figure 3.23(a) shows results for steel AISI E9310. As seen, the mean shear stress, τc does not depend on the cutting speed and on the rake angle. The same results were obtained using various tool materials, geometry and work materials (Fig. 3.23(b)). These facts cannot be explained using the traditional notions used today to explain metal cutting phenomena. For example, although the contact temperature at the tool–chip interface

158

Tribology of Metal Cutting tc(MPa) − gn = −10°

− gn = 0°

− gn = 10°

− gn = 20°

(a)

400

200 0

160

480 n (m/min)

320

tc(MPa) 1 400 2 3

(b)

4

5

200 6 7

0

80

160

240

320

n (m/min)

Fig. 3.23. Influence of cutting speed (ν) on the mean shear stress (τc ): (a) under different rake angles in machining steel AISI E9310, tool material P20 (79% WC, 15% TiC, 6% Co); (b) for various work materials: 1 – beryllium copper UNSC17000, HB320, 2 – beryllium copper UNSC17000, HB200 and steel AISI O7 (1.2% C) annealed, 3 – steel AISI E9310, 4 – beryllium copper UNSC17000, HB110, 5 – Armco iron, 6 – copper and 7 – cadmium.

varies considerably over the range of the cutting speeds used in the tests (Figs. 3.23(a) and (b)), the mean shear stress, τc does not change. This is in direct contradiction with the notions on material behavior used in the traditional metal cutting considerations where the properties of the work material obtained in the standard mechanical testing are used to judge the cutting parameters. Figures 3.24(a) and (b) explain this issue. As seen, the mean shear stress, τc does not depend on the contact temperature over a wide range of cutting conditions while the same property (the shear strength) obtained in a standard tensile test is significantly temperature dependent. The experimental results discussed show that the mean shear stress is work material specific and does not depend on the rake angle and cutting regime (speed and feed). This can be easily explained with the generalized model of chip formation (Chapter 1). According to this model, metal cutting is a cold-working process where the state of stress in the deformation zone should be sufficient to cause the purposeful fracture of the layer being removed. The required state of stress in the deformation zone is achieved due to the spatial arrangements of the components of the cutting system and due to the load

500

1

2

600

700

(a)

800

f = 0.156 mm/rev f = 0.205 mm/rev f = 0.314 mm/rev f = 0.402 mm/rev

900 qc (°C)

f = 0.510 mm/rev f = 0.610 mm/rev f = 0.850 mm/rev f = 1.420 mm/rev f = 2.380 mm/rev

1

500

0

200

400

2

700

(b)

f = 0.510 mm/rev

f = 0.156 mm/rev

900

qc (°C)

Fig. 3.24. Comparison of the influence of contact temperature (θc ) on the mean shear stress (τc ) and on the shear strength in tensile testing (curves 1 and 2): (a) work material: steel AISI 1050, curve 1 – test results at shear strain 0.15 and curve 2 – test results at shear strain 0.75, (b) work material: steel ASTM A514 (0.18% C, 1.1% Cr, 1.3% Ni), curve 1 – test results at shear strain of 0.33 and curve 2 – test results at shear strain of 1.8.

0

100

200

tc(MPa)

tc(MPa)

Tribology of the Tool–Chip and Tool–Workpiece Interfaces 159

160

Tribology of Metal Cutting

applied by the cutting tool which is transmitted to the deformation zone through the tool–chip interface. Because the combined stress that causes the fracture of the layer being removed depends primarily on the mechanical properties of the work material, the mean shear stresses at the tool–chip interface should be the same regardless of the conditions achieved at the tool–chip interface. Analyzing numerous experimental results, Poletica concluded [69] that, although the mean shear stress at the tool–chip interface can be correlated with many mechanical properties of the work material, the best fit seems to be achieved with the ultimate tensile strength, σUTS as shown in Fig. 3.25. He concluded that the following empirical relation shows good correlation τc = 0.28σUTS

(3.52)

The independence of the mean shear stress at the tool–chip interface on many factors that affect the cutting process is an important characteristic of this process. Among other factors, the most surprising and seemingly paradoxical is the independence of this stress on the mean contact temperature at the tool–chip interface. Zorev [2] and partially Spaans [80] attempted to explain this paradox by mutual influence of two reverseproportional factors, namely the strain rate and temperature. The following explanation has been offered: the lowering of the mean shear stress at the tool–chip interface with the contact temperature is fully compensated by the growth of this stress due to the

tc(MPa)

Beryllium copper, HB320

400 Steel AISI 07

Steel ASTM A514

Beryllium copper, HB200 Beryllium copper, HB110

200 Armco iron Copper

Cadmium

0 0

800

sUTS (MPa)

Fig. 3.25. Correlation between the mean shear stress at the tool–chip interface (τc ) and the ultimate tensile strength (σUTS ) for different work materials.

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

161

corresponding increase in the strain rate. In other words, the effect of temperature on the mean shear stress at tool–chip interface is balanced by the strain rate effect in such a way that this stress remains constant. This idea, however, was criticized by Poletica [69] who conclusively proved that this is not the case in metal cutting. The total friction force on the tool rake face (Fig. 3.21(a)) then can be calculated as F = τc lc dw1

(3.53)

Substituting Eqs. (3.42) and (3.52) into Eq. (3.53), one can obtain Ff = 0.28σUTS t1 dw1 ζ kt

(3.54)

Bearing in mind that dw1 = dw and dividing both sides of Eq. (3.54) by Aw = t1 dw (the uncut chip cross-sectional area) and rearranging, one can obtain ζ=



1 (0.28σUTS

)1/ kt

Ff Aw

1/ kt

=

1 (0.28σUTS )1/ kt

(τc )1/ kt

(3.55)

This equation establishes the direct correlation between the mean shear stress and CCR, although some researchers argued that this correlation is linear [69]. On the contrary, to the mean shear stress, the mean normal stress σc at the tool–chip interface, is very sensitive to many parameters of the cutting process. Being work material specific, this stress depends mainly on the cutting speed, cutting feed and cutting tool rake angle. Having conducted a great number of cutting tests, Zorev [2] and Poletica [69] conclusively proved that the mean normal stress at the tool–chip interface increases with the cutting speed for a wide range of metallic work materials. Figure 3.26 shows the test results for various steels. As seen, the influence is more pronounced for high-carbon steels having higher hardness and strain rate sensitivity. One may argue, however, that the metallurgy of these steels may also contribute to the obtained result. To show that this is not the case, Fig. 3.27 presents the results for beryllium copper of different hardness. As seen, the mean normal stress at the tool–chip interface increases with the hardness of the work material. It was found that the mean normal stress at the tool–chip interface decreases with the rake angle. It can best be illustrated with the experimental results obtained in the machining of cadmium shown in Fig. 3.28(a) because CCR hardly changes with this work material although the rake angle varies in a very wide range, namely from −40 to +60◦. Therefore, data presented in this figure may be regarded as that obtained with invariable CCR. As seen, the mean normal stress decreases with the rake angle. This phenomenon can readily be explained using the above-discussed definition of the cutting process. Because cracks form at points A and O (Fig. 3.21) due to the combined action of compressive and bending stresses, the maximum combined stress at these points forms due to compressive force and bending moment imposed by the resultant force R. As such, the compressive force is determined by the tool–chip contact area while the bending moment

162

Tribology of Metal Cutting sc (MPa) 6 600 5

400 4 3 200

2 1

0 20

100

180

260

n(m/min)

Fig. 3.26. Influence of cutting speed (ν) on the mean normal contact stress (σc ) for various steels: 1 – steel 1010, 2 – steel 1020, 3 – steel 1060, 4 – steel HV100 (0.2% C, 3.8% Ni, 1.5% Cr), 5 – steel ASTM A228 (0.8% C) and 6 – tool steel 07 (1.2% C). Tool: carbide P20 (79% WC, 15% TiC, 6% Co), normal rake angle γn = 10◦ and cutting feed f = 0.156 mm/rev. sc(MPa)

HB320 f = 0.07 mm/rev f = 0.15 mm/rev

1200

900

HB200 f = 0.07 mm/rev f = 0.15 mm/rev f = 0.26 mm/rev f = 0.34 mm/rev

600

300

HB110 f = 0.07 mm/rev f = 0.15 mm/rev f = 0.26 mm/rev f = 0.34 mm/rev

0 0

80

160

n(m/min)

Fig. 3.27. Influence of cutting speed (ν) on the mean normal contact stress (σc ) for beryllium copper UNSC17000 of different hardnesses. Tool: carbide P20 (79% WC, 15% TiC, 6% Co), normal rake angle γn = 10◦ and cutting edge angle κr = 70◦ .

Tribology of the Tool–Chip and Tool–Workpiece Interfaces sc (MPa) tc(MPa)

163

Normal stress sc Tangential stress tc

200

(a) 100

0

−40

−20

0

20

40

gn(°)

sc(MPa) gn = −10° gn = 0° gn = −10° gn = −20°

600

(b)

400

200

0 0

4

6

8

10

Po

Fig. 3.28. Mean normal contact stress as a functions of: (a) the tool normal rake angle (γn ), work material – cadmium, tool material – carbide M30 (92% WC, 8% Co), cutting speed ν = 40.2 m/min, cutting feed f = 0.67 mm/rev and depth of cut dw = 2 mm; (b) Po-criterion for different rake angles tool material – carbide P20 (79% WC, 15% TiC, 6% Co), work material – steel ASTM A514 (0.18% C, 1.1% Cr, 1.3% Ni), cutting edge angle κr = 70◦ , depth of cut dw = 3 mm and cutting feed f = 0.07–0.43 mm/rev.

is determined by both the contact area and the arm of the normal force with respect to the mentioned points. Because a given work material fails at points A and O under the same combined stress, the bending in this combined stress is a kind of constant for this work material. Therefore, if the arm of the normal force creating the bending moment (stress) increases due to an increase in the rake angle, the normal contact stress decreases accordingly to keep the same needed bending stress. Figure 3.28(b) provides further experimental support to the discussed model of the correlation amongst the parameters of the tool–chip interface. The relationship between the mean normal stress and the Po-criterion has more general character than that drawn directly from Fig. 3.27. Figure 3.29 shows the data for different

164

Tribology of Metal Cutting

sc(MPa) Beryllium copper, HB 320, Tool - carbide M30 1200

Steel AISI 07, Tool - carbide P20 Copper, Tool - HSS M42 Beryllium copper, HB 310, Tool - carbide M30 Beryllium copper, HB 200, Tool - carbide M30

800

Steel ASTM A514, Tool - carbide P10 Steel 1010 HB100, Tool - carbide M30 Steel 1020 HB130, Tool - carbide M30

400

0

0

4

8

12

16

20

Po

Fig. 3.29. Influence of Poletica criterion on the mean normal contact stress for various work materials. Tools with γn = 10◦ .

work materials. As seen, regardless of a wide range of the mechanical characteristics of the work materials (HB33–220), all experimental points are close to a single curve. The same results were obtained by Zorev [2] with AISI steels 1010, 1020 and E9310. Summarizing the obtained experimental results, one can conclude that not only the uncut chip thickness and cutting speed but also the mechanical properties of the work material affect the mean normal stress insomuch as they affect the Po-criterion. A particular value of the Po-criterion affects the normal stress at the tool–rake face. As this criterion decreases, the mean normal stress increases. The mean contact stress, therefore, is a function (and a characteristic) of the state of stress in the contact zone. It depends on the Po-criterion in the same way as this criterion affects the state of stress in the contact zone. Function σc = f (Po) shown in Fig. 3.29 has the hyperbolic shape and with reasonable accuracy can be approximated as σc =

180 (Po)0.95

(3.56)

which, in the general case, can be represented as σc =

Aγ (Po)mγ

(3.57)

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

165

where coefficient Aγ and power mγ are determined by the rake angle. As such, normally mγ < 1 and Aγ decreases with the rake angle. Substituting Eq. (3.42) into Eq. (3.57), one can obtain σc =

Aγ (ζ)kt mγ

(3.58)

or N = Aγ t1 dw ζ kt (1−mγ )

(3.59)

Because mγ is close to 1, the power of CCR is very small. Therefore, for a given uncut chip cross-sectional area (t1 × dw ), the normal force on the tool–rake face is primarily a function of the tool–rake angle and only weakly depends on CCR. Influence of tool material. Of the many properties of the work material, elastic characteristics, thermophysical properties (primarily, thermoconductivity) and chemical properties play the most significant role in the contact process at the tool–chip and tool–workpiece interfaces. Elastic deformation of the cutting wedge due to the normal contact stress may play a significant role for wedges having high rake angles. Normally, it does not affect significantly the distribution of the normal and shear stresses on the tool–chip interface. Experimental studies of the influence of various thermophysical properties of the tool material on the tribology of the tool–chip interface are very complicated, so it requires vast experience and knowledge on the relevant properties of the work and tool materials. This is because the selection of the pairs “tool–work” materials has to be accomplished in a certain sequence when one property is altered while the other remains the same. It cannot be accomplished within the tool and work materials normally used in the practice of machining. Therefore, copper, lead and aluminum were used in the experimental studies as work materials to obtain tool materials with various desired properties, which normally cannot be used as tool materials due to their insufficient hardness and low hot hardness. To evaluate the separate influence of thermoconductivity and chemical properties of the tool material on the contact characteristics, Poletica [69] proposed to use lead as the work material. The prime cause for this selection is because lead is chemically passive. Moreover, it does not form solid-state solutions with materials used in machining. Exceptions are some “soft” materials as magnesium, tin, cadmium and antimony as well as noble materials as gold and silver. Therefore, lead can be considered as chemically inactive (inert) with respect to the tool material. Among similar soft materials, lead is characterized by low thermoconductivity that assures relatively high cutting temperatures and it allows clearly distinguishing the influence of thermoconductivity of tool materials on the contact process. Tests with lead as the work material were carried out using the same tool geometry, cutting feed and the depth of cut. Figure 3.30(a) shows the results obtained using various tool materials. The experimental points correspond to the invariable cutting speed.

166

Tribology of Metal Cutting

z Beryllium copper

(a)

4.5 Carbide M30 (92%WC, 8%Co)

Ti Grade 1

Carbide P20 (79%WC, 15%TiC, 6%Co) HSS M42

4.0 0

34

68

ktm(W/mK)

z Carbide M30

(b)

2.0 Carbide P20 Carbide P10 Carbide P30 1.5 0

34

ktm(W/mK)

Fig. 3.30. Influence of thermoconductivity of the tool material (ktm ) on CCR: (a) work material – lead and (b) work material – steel AISI 1055.

Figure 3.30(b) shows the results for steel AISI 1055. As seen, CCR, and thus the amount of work of plastic deformation in metal cutting, increases when the thermoconductivity of the tool material increases. When this is the case, the mean temperature at the tool– chip interface increases. Therefore, it can be suggested that the relationships shown in Figs. 3.30(a) and (b) represent the dependence of CCR on the mean contact temperature. Unfortunately, the experimental results presented in Fig. 3.31(a) do not support this suggestion. As seen, if the mean contact temperature is kept invariable, CCR still depends on the thermoconductivity of the tool material (Fig. 3.31(b)). It can be concluded, therefore, that the thermoconductivity of the tool material has a more complicated physical mechanism of influence on CCR and hence on the work of plastic deformation in cutting. The trend, however, is still the same: the greater the thermoconductivity of the tool material, the higher is the CCR. Any change in the mean contact temperature leads to the corresponding change in the contact pressure at the tool–chip interface. Moreover, this pressure also changes when the distribution of the contact temperature changes. The thermoconductivity of the tool materials has the greatest influence on the distribution of the contact temperature. The results of a great number of cutting tests with diamond tools showed [69] that a great increase in the thermoconductivity of the tool material leads to a significant shift of the maximum

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

167

z 1 13

4

11

(a) 2 3

9 5 7 0

40

120

200

qc (°C)

z (b)

10

8 0

20

40

60

80

ktm (W/mK)

Fig. 3.31. Influence of mean contact temperature on the CCR for different tool materials: 1 – beryllium copper UNSC17000, 2 – tungsten, 3 – high-speed steel M42, 4 – high manganese steel and 5 – Ti Grade 1; work material – lead.

contact temperature towards the cutting edge. As such, the average contact temperature decreases which, in turn, leads to the corresponding increase in the tool–chip contact length. The influence of these two factors lowers the tool life when machining the steel materials, i.e. when the contact stress and temperature are high. In the author’s opinion, this is the major cause of very poor tool life of diamond tool in the machining of steels, although practically all the known literature sources on metal cutting (for example, see Ref. [37]) state that the prime cause for this is the transformation of diamond to a graphite form and/or interaction between diamond and iron and the atmosphere. The latter suggestion cannot explain very poor tool life of these tools in the machining of nickel alloys, practically having no carbon and iron. Mutual adhesion properties of the work and tool materials. Analyzing a great body of research works done in the field of the adhesion phenomenon that occurred in the contact of two materials, Poletica concluded [69] that their results can hardly be applicable in metal cutting because most of these were obtained using conditions that are not particularly for metal cutting. For example, the results obtained using pin-on-disc machines (discussed in Chapter 6) cannot be applicable in metal cutting at all (see Chapter 6). Poletica also concluded [69] that solubility of the work and tool materials is the major contributing factor in their adhesion interactions. Therefore, the only proper way to assess

168

Tribology of Metal Cutting Table 3.1. Properties of copper in terms of its ability to form solid-state solutions.

Material (component)

Mutual solubility Liquid state

In solid state In copper In material (wt.%/at.%) (wt.%/at.%)

Aluminum Tungsten Iron Cobalt Manganese Molybdenum Nickel Titanium Chromium Silicon Carbon

Unlimited Unlimited Unlimited Unlimited Unlimited Insoluble Unlimited Insoluble Limited Unlimited Insoluble

9.4/19.6 9.4/19.6 9.4/19.6 12.8/42.0 31/25 Insoluble Unlimited 4.3/5.6 Insoluble 4.5/10 Insoluble

5.7/2.5 Insoluble 8.5/7.5 4.1/3.4 Unlimited Insoluble Unlimited 2.1/1.6 Insoluble Insoluble Insoluble

Formation of intermetallic compounds

Cu3 Al4 and others No No No No No No Ti2 Cu, TiCu No Cu2 Si and others No

adhesion interactions between work and tool materials is to test a single work material against several tool materials purposefully selected as having distinctive properties in terms of their solubility of solid phases. Copper was selected as the work material. This is because copper forms solid solution with a number of relatively hard materials. In machining copper, the selection of tool materials is not very restricted (in terms of their hot hardness and allowable temperature). Copper has low hardness and high thermoconductivity. Table 3.1 illustrates the properties of copper in terms of its ability to form solid-sate solutions. Technically pure tungsten, titanium alloy Ti Grade 1 and beryllium copper were selected as tool materials. The first one was selected because it is totally neutral to copper. Ti Grade 1 contains 90% of Ti, which has very limited solubility in copper and can form chemical compounds with copper. Beryllium copper contains about 98% of copper and thus should have the maximum affinity. Single-point cutting tools made of Ti Grade 1 and beryllium copper were heat-treated to hardness HB360 and ground with rake angle γ = 25◦ . Tungsten tools were ground with γ = 10◦ because of the high brittleness of tungsten. The test results shown in Figs. 3.32 and 3.33 indicate that the adhesion properties of the tool material with respect to the work material have a marked influence on the tool–chip contact length and CCR. As seen, the contact length increases 5.5 times and CCR – almost 4 times when the beryllium copper tool is used when compared to the tungsten tool. Figures 3.34(a) and (b) show significant influence of adhesion properties of the tool material on the mean normal contact stress and on the ratio of the mean shear and normal contact stresses. There are no data for the tungsten tool in these figures because this tool has a different rake angle having its own influence on these parameters. As seen, the mean shear stress in machining with the Ti Grade 1 tool is three times higher than

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

169

lc(mm) Beryllium copper Ti Grade 1

Tungsten

4

2

0 1.4

0

2.8

n (m/s)

Fig. 3.32. The tool–chip contact length in machining copper with three selected tool materials having considerably different adhesion properties. The depth of cut dw = 4 mm and feed f = 0.17 mm/rev.

z Beryllium copper

Tungsten

Ti Grade 1

20

12

4 0

40

80

120 n (m/min)

Fig. 3.33. CCR in machining copper with three selected tool materials having considerably different adhesion properties. The depth of cut dw = 3 mm, feed f = 0.17 mm/rev, tool cutting edge angle κr = 70◦ and inclination angle λp = 0◦ .

that of machining with the tool made of beryllium copper. As such, the ratio of the mean shear and normal contact stresses is 2–2.5 times higher. Although the contact length, mean normal contact stress and CCR in machining with different tool materials vary significantly as seen in Figs. 3.32–3.34, the mean shear stress remains practically the same as seen in Fig. 3.35. As before (see explanations to Fig. 3.23), it is explained by the fact that this stress depends only on the properties of the work material. When machining the work material with a tool having different adhesion properties, the influence of tool material would be different. Figure 3.36 shows the results of a test

170

Tribology of Metal Cutting

sc (MPa) 100

(a)

0

tc /sc 2

(b) 1 Beryllium copper 0

80

Ti Grade 1 160 n (m/min)

Fig. 3.34. Influence of cutting speed in machining copper: (a) on the mean normal contact stress at the tool–chip interface, (b) on the ratio of the mean shear to the mean normal contact stresses. Rake angle γ = 25◦ , depth of cut dw = 3 mm, feed f = (0.07–0.3) mm/rev, tool cutting edge angle κr = 70◦ and inclination angle λp = 0◦ .

tc (MPa) Beryllium copper 300 Ti Grade 1

- s = 0.07 mm/rev - s = 0.17 mm/rev - s = 0.30 mm/rev - s = 0.07 mm/rev - s = 0.17 mm/rev - s = 0.30 mm/rev

200

100 0

80

160

n (m/min)

Fig. 3.35. Influence of cutting speed on the mean shear stress in machining copper.

where CCR for aluminum were determined as a function of the cutting speed using the beryllium copper and steel tools. Iron is much more chemically active to aluminum than copper. As a result, higher CCRs were obtained for the steel tool compared to the beryllium copper tool although the thermoconductivity of the beryllium copper tool is much higher than that of the steel tool. The above-discussed test results illustrate the mutual action of thermoconductivity and adhesion properties. To separate these two issues, the tools used in these experiments were plated with a very thin layer of chromium. This layer could not change the

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

171

z Beryllium copper Steel AISI 07

16

12

8 0

160

320

n(m/min)

Fig. 3.36. Influence of cutting speed on the chip compression ratio in machining aluminum for two different tool materials. Rake angle γ = 20◦ , depth of cut dw = 2 mm, feed f = 0.21 mm/rev and tool cutting edge angle κr = 45◦ .

thermoconductivity significantly while it significantly affected the adhesion properties at the tool–chip contact. The test results are shown in Fig. 3.37. As seen, CCR for the plated beryllium copper tool is much smaller than that for the non-plated one. In the case of titanium tool, the difference is rather small. For the tungsten tool, the result was the opposite and the difference is significant. Influence of mechanical properties of the work material. It is much easier to study the influence of mechanical properties of work material on the tribological conditions at the tool–chip interface than that of the chemical composition of the work and tool materials. The mechanical properties of the work material can be altered in a wide range by its heat treatment. Poletica proposed [69] the use of beryllium copper as the work material. As mentioned above, it is an excellent test material because its mechanical properties can be changed over a wide range by heat treatment while the phase composition and microstructural parameters remain practically unchanged. The test results with beryllium copper are shown in Figs. 3.18, 3.19(b), 3.23(b), 3.27 and 3.29. Figure 3.38 shows the contact characteristics obtained under invariable average contact temperature as functions of the true stress at the fracture of the work material represented by the hardness of the work material [69,81]. As it follows from Fig. 3.38, the mean normal stress, σc increases with the hardness of the work material. The mean shear stress τc also increases in proportion to the hardness. The latter result, obtained under special test conditions, is part of a more general dependence shown in Fig. 3.25 where this stress is correlated with the strength of various work materials. Therefore, the results shown in Figs. 3.38 and 3.25 complement each other.

172

Tribology of Metal Cutting

z 1 - Beryllium copper 2 - Ti Grade 1 3 - Tungsten Non-plated

20

Cr-plated

16 1 12

8

4

2 3

0 0

80

160

n (m/min)

Fig. 3.37. Influence of cutting speed on CCR in machining copper with the non-plated and Cr-plated tools. Rake angle γ = 20◦ , depth of cut dw = 2 mm, feed f = 0.15 mm/rev and tool cutting edge angle κr = 45◦ .

Contact Stress (MPa)

Po

sc 6

1200 Po

800

4

400

2

tc 800

1000

1200

1400

sf (MPa)

Fig. 3.38. Contact characteristics in machining beryllium copper as functions or its hardness represented by the true stress at fracture. Rake angle γ = 10◦ , tool cutting edge angle κr = 45◦ , feed f = 0.15 mm/rev and cutting speed ν = 1.67 m/s.

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

173

z 1

2 8

5

3

4

7

4

6 8

10

9

0 0

80

160

n (m/min)

Fig. 3.39. Influence of cutting speed on CCR in machining of various materials: 1 – steel AISI 1010, 2 – copper, 3 – aluminum 2014, 4 – lead, 5 – Armco iron, 6 – forging brass UNS C37700, 7 – steel ASTM A514 (0.18% C, 1.1% Cr, 1.3% Ni), 8 – steel AISI 07, 9 –Ti Grade 1 and 10 – cadmium.

It follows from the results shown in Fig. 3.38 that the apparent friction coefficient at the tool–chip interface calculated as the ratio of the shear and normal contact stresses, depends primarily on the hardness of the work material and, secondarily, on other properties of the work and tool materials and the machining regime. Figure 3.39 shows the experimental results for various work materials. These materials differ not only in mechanical properties but also in many other physical and chemical properties. As such, only the mean shear stress would depend on the strength of the work material while other tribological characteristics at the tool–chip interface can vary in wide ranges. As such, CCR would depend only on the mutual adhesion properties of the work and tool materials. As seen in Fig 3.39, CCR is practically the same in machining work materials having considerably different mechanical properties such as cadmium and titanium alloy. At the same time, CCRs for steel AISI 07 and Ti Grade 1 are different although these work materials have approximately the same mechanical properties. Influence of surrounding medium. The cutting process can take place in different media. The most common media are gases and liquids. Although influence of medium is often treated as the influence of cutting fluid (as discussed in Chapter 6), one important aspect of the influence of the surrounding medium on the tribological conditions at the tool–chip interface, namely the influence of atmospheric air is discussed here. While cutting in the presence of air, one might expect the occurrence of certain chemical reactions of oxygen and nitrogen contained in the air with freshly formed surfaces of the work and tool materials. It is a strong belief among the metal cutting specialists that the formation of

174

Tribology of Metal Cutting

oxidized, nitrogenized and oxi-nitrogenized films and water vapor on the contact surfaces are the results of such reactions. To clarify this long-standing issue, a series of tests were carried out in air and under inert gas using a specially designed pressure chamber [69] installed on a lathe. The chamber was filled with argon with a slightly higher (by 0.05 MPa) pressure than the atmospheric pressure. The actual pressure of argon in the chamber was controlled by a manometer. Two work materials were selected for the test, namely Armco iron and copper since they were having very high sensitivity to the properties of the medium in cutting. Moreover, copper has an extremely high sensitivity to oxygen that should be very helpful in detecting any influence of oxygen in the air on the cutting process. The test results are shown in Fig. 3.40. No difference in CCR and thus in the tool–chip contact length was found. The only difference that was observed is the absence of temper colors on the chip obtained in cutting with argon. Although it is incorrect to extend the obtained result for all kinds of work materials, particularly in the case of machining some titanium alloys as pointed out by Poletica [69], it allows the conclusion that disproves the above-mentioned common belief on the influence of oxygen in metal cutting.

z Copper 12

Air 8

Argon

Armco iron 4

0 20

60

100

n(m/min)

Fig. 3.40. Influence of the medium on CCR. Cutting feed f = 0.10 mm/rev and depth of cut, dw = 3 mm.

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

175

3.2.5 Generalizations The results of the theoretical and experimental studies on the tribological conditions at the tool–chip interface can be summarized as follows: • The concept of the coefficient of friction is inadequate to characterize the sliding between the chip and tool and thus should not be used in metal cutting studies. The known modeling of metal cutting where a constant friction coefficient is used (practically all commercial software packages) cannot be considered as adequate to any real cutting process. Instead, contact stresses at the tool–chip interface and their dependence on the parameters of the cutting process should be considered. • There is a great discrepancy in the reported theoretical and experimental results on the distribution of the normal and shear stresses over the tool–chip interface. The most recently reported uniform distribution of the normal and shear contact stresses is in direct contradiction with the known experimental results and everyday practice of metal cutting. • The tool–chip interface can be conditionally divided into two approximately equal distinctive parts: plastic and elastic. • Because the chip formation process is of a cyclic nature, the normal and shear stresses as well as the shape of their distributions vary within each cycle of the chip formation. Therefore, the mean normal and shear stresses at the tool–chip interface are of prime interest in metal cutting. These parameters should be considered in the process analysis and optimization. • The length of the tool–chip interface depends both on the uncut chip thickness and rake angle. The dependence of the contact length on the cutting speed directly resembles the dependence of CCR on the cutting speed. • The contact length is directly proportional to the uncut chip thickness for different work materials. One of the most important tribological characteristics at the tool– chip interface is the ratio of the contact length to the uncut chip thickness referred as the Po-criterion. This criterion remains invariant to changes in the mechanical and physical properties of the work material. • There is a direct correlation between the Po-criterion and CCR. This correlation is expressed by Eq. (3.42). Moreover, it represents the condition of static equilibrium of the chip. • The normal and shear stresses at the restricted rake face is always higher than those with the natural contact length. The discussed increase can be readily determined by the condition of static equilibrium. • The mean shear stress at the tool–chip interface is a function of properties of the work material. It does not depend on the tool geometry, tool material and cutting feed. Among other factors, the most surprising, and seemingly paradoxical, is the independence of this stress on the mean contact temperature at the tool–chip interface. The mean shear stress is well correlated with the ultimate tensile strength of the work material. The listed unique properties of the mean shear

176

Tribology of Metal Cutting stress should be considered the second (next to CCR) stable important tribological characteristic of the tool–chip interface. Knowing CCR and the mean shear stress at the tool–chip interface, one can easily calculate 80–90% of the energy spent in the cutting system. Moreover, because the mean shear contact stress determines to a large extent the temperature at the tool–chip contact, it can be stated that this temperature is solely a function of the cutting speed and the work material.

• The mean normal stress at the tool–chip interface is very sensitive to many parameters of the cutting process. Being work material specific, this stress depends mainly on the cutting speed, cutting feed and cutting tool rake angle. This stress increases with the cutting speed for a wide range of metallic work materials and decreases with the rake angle. The mean contact stress was found to be a function (and a characteristic) of the state of stress in a contact zone. It depends on the Po-criterion in the same way as this criterion affects the state of stress in the deformation zone. Moreover, for a wide range of work materials, the mean normal stress at the tool–chip interface is uniquely related to the Po-criterion. • Among many properties of the tool material, the greatest influence on the contact conditions at the tool–chip interface is its thermoconductivity and adhesion properties while the influence of the elastic constants of the tool material are small. • The influence of thermoconductivity on the tribological conditions at the tool–chip interface manifests in two ways. First, it affects the mean contact temperature, and second, – it affects the temperature distribution over this interface. • The CCR and thus the amount of work of plastic deformation in metal cutting increases when the thermoconductivity of the tool material increases. When the thermoconductivity of the tool material increases, the average temperature at the tool–chip interface increases. Therefore, it can be suggested that the relationships shown in Figs. 3.30(a) and (b) represent the dependence of CCR on the average contact temperature. The greater the thermoconductivity of the tool material, the higher is the CCR. • Any change in the average contact temperature leads to the corresponding change in the contact pressure at the tool–chip interface. Moreover, this pressure also changes when the distribution of the contact temperature changes. The thermoconductivity of the tool materials has the greatest influence on the distribution of the contact temperature. • The adhesion conditions at the tool–chip interface affect the cutting process in terms of energy spent much more than considered today in the literature on metal cutting. As such, the solubility of the work and tool materials is the major contributing factor in their adhesion interactions. • The mutual adhesion properties of the work and tool materials should be carefully considered in the selection of the tool material for a given application. A small alternation in the chemical composition of the work material (often the case in the automotive industry) can change these properties significantly resulting in a significant variation in the energy spent in cutting and thus in tool life. • The same coating material applied for a different substrate can cause significant decrease or increase not only in the energy spent at the tool–chip interface, but also

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

177

in the energy of plastic deformation of the layer being removed. Therefore, the properties of the combination “substrate-coating” should always be considered. Unfortunately, this fact is not appreciated in the selection of the substrate and coating materials. As a result, there are many “unexplainable” (by metal cutting practitioners and coating application specialists) significant difference in the results on the performance of “the same” coating under “similar” conditions. 3.3 Tool–Workpiece interface 3.3.1 Zorev’s results The contact phenomena on the tool flank surface are of interest because their understanding allows the explanation of tool flank wear and the formation of the major characteristics of the machined surface. Nevertheless, there are few known studies on the matter available. Surprisingly, modern books on metal cutting do not consider these phenomena. The flank wear is considered using the age old Taylor’s tool life equation having a phenomenological nature. Another way to look at the problem is to understand the physical processes taking place at the tool–workpiece interface called the flank contact area. Although the contact processes on the tool flank are determined by the normal and frictional forces acting at the tool– workpiece interface, the ratio of the normal and contact forces does not follow those obtained in the standard mechanical tests due to complexity of the contact process on this interface. These processes include severe friction and plastic deformation of the machined surface. A comprehensive analysis of the attempts to derive analytical expression for the flank forces is presented by Zorev [2]. He came to a surprising conclusion that if the flank wear is small, the depth of cut is great and the workpiece hardness is “moderate,” then the forces on the flank may not be taken into consideration because they are small in comparison with those on the rake face. On the contrary, if flank wear is large, the depth of cut is small, particularly when machining hard materials, the flank forces become comparable with the forces on the tool rake. As such, the normal force on the flank face of the major cutting edge can be calculated as Nf = σc−f



dw HB dw hf ≈ hf kg/mm2 sin κr 3 sin κr

The friction force on this face is    

dw dw + f ≈ 0.2HB +f kg/mm2 Ff = µff σc−f sin κr sin κr

(3.60)

(3.61)

and the normal force on the flank surface of the minor cutting edge calculates as Nf =



HB f hf1 kg/mm2 , 3

(3.62)

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Tribology of Metal Cutting

where HB is Brinell hardness of the work material, hf and hf1 are the widths of the flank contact surfaces of the major and minor cutting edges, respectively, σc−f is the mean normal contact stress at the tool–workpiece interface and µff is the apparent friction coefficient at this interface. The mean normal (σc−f ) and shear (τc−f ) stresses on the flank face contact area are calculated as

HB ≈ σUTS kg/mm2 3

≈ 0.2HB ≈ 0.6σUTS kg/mm2

σc−f ≈ τc−f

(3.63) (3.64)

According to the initial Zorev’s analysis [2], these stresses do not depend on the cutting regime and type of tool material. Having noticed this discrepancy later, Zorev carried out a great number of cutting tests to establish the above-mentioned dependences. More than 20 different work materials having hardness from HB80 (annealed pure iron) to HRC 65 (quench-hardened steel) were tested. Figure 3.41 shows the experimental results for cutting speeds that correspond to a 90-min tool life. In Zorev’s opinion [2], the reduction of σc−f with decreasing the cutting speed is attributed to the “secondary shear” on the

20

30

40

50

60

HRC

sc−f (MPa)

Cast iron - M30

4000

3200

2400

sc−f (MPa) dw = 0.1 mm 1800

1600

1.0 mm

800

Steel - P01

Steel - P20

0.5 mm 1200

600

2.0 mm 0 100 100

0 200 600

300

400

800 1000 1200 1400

HB (kg/mm2)

sUTS (MPa)

Fig. 3.41. Contact stress at the tool–workpiece interface according to Zorev.

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

179

rake face, which protects the flank contact surface. The same explanation is provided for the influence of depth of cut, dw : if tool life is kept constant, the cutting speed decreases as the depth of cut increases. This statement is, however, in direct contradiction with Zorev’s experiments on tool life (criterion – the width of the flank wear land) where increased cutting speed resulted in a longer tool life [2]. Another important experimental fact should be noted in Fig. 3.41, namely, the influence of tool material. For the same tool life, the contact stress σc−f and thus the forces on the flank contact face for the less wear-resistant carbide P01 are approximately 25% lower than for more wear-resistant P20 carbide. Nevertheless, Zorev recommended [2] using the same apparent coefficient of friction µff = 0.6 for calculating the flank frictional force regardless of tool material and other cutting conditions.

3.3.2 Assessment of tribological characteristics Major tribological characteristics. According to a generally accepted hypothesis, the contact between the tool flank and the workpiece machined surface occurs due to the elastic recovery (or spring back) caused by plastic deformation of this surface in cutting. Figure 3.42(a) shows an idealized case where the cutting tool is perfectly sharp as commonly assumed in the most known modeling of the metal cutting process (see Fig. 1.1). The radial cutting force FT (the complete force diagram is considered in Fig. 1.1(c)) causes the plastic deformation of the machined surface which, after the cutting edge passes over this surface, recovers by δ1 causing the contact with the tool flank up to point A. The elastic recovery, therefore, should be proportional to this radial cutting force, which, in turn, depends to a large extent on the uncut chip thickness t1 . The cutting edge of any real tool, however, is not perfectly sharp so that a much real contact picture is shown in Fig. 3.42(b). In this figure, the cutting edge radius forms

t1

a A

Fc

d1

Tool B C FT

F E Workpiece FfF

D

Workpiece

FfN

(a)

(b)

Fig. 3.42. Contact of the tool flank with the workpiece: (a) ideally sharp tool as assumed in modeling and (b) real contact with the tool–workpiece interface.

180

Tribology of Metal Cutting

the transition curve BD between the rake and the flank surfaces. This makes the position of point C uncertain, where the chip separates from the workpiece. The wear land DE is also present in any real cutting tool or, at least, it forms in the first few seconds of machining. Part EF represents the flank–workpiece contact surface. If the radius of the cutting edge is small, the normal (FfN ) and the friction (FfF ) forces acting on the flank are results of the interactions between the wear land DE and the machined surface of the workpiece. The basic tribological characteristics of the tool–workpiece interface are: • The sliding velocity which is normally equal to the cutting speed. In some special tools, where the feed velocity(ies) is significant, the magnitude of this velocity is equal to the magnitude of the resultant velocity of a considered point of the cutting edge. • The contact length – the margin and then, after some time of cutting, the margin and flank wear length of the tool–chip contact, hf . • The friction force, FfF . • The specific frictional force which is the mean shear stress τc−f =

FfF , hf lce−a

(3.65)

where lce−a is the active length of the cutting edge. Normally, lce−a = dw /sin κr . • The normal force at the tool–workpiece interface, FfN . • Mean contact stress at the tool–workpiece interface σc−f =

FfN hf lce−a

(3.66)

• Mean contact temperature at the tool–workpiece interface, θfl−av . Experimental studies. Any experimental method of evaluation of contact stresses has its “sensitivity” evaluated by the minimum contact area for which it is yet still possible to obtain reliable data on contact stress distribution. The area of the contact surface on the tool flank face of a “sharp” tool is very small, so it is out of range of modern experimental methods for contact stress distribution. Therefore, the evaluation of contact stresses is possible for a tool having appreciable natural (due to tool wear) or artificially made (for a study) wear land on the tool flank surface. Poletica [69] studied the contact stresses on the tool flank using the photoelastic method. A series of turning and orthogonal cutting (shaping on a milling machine) tests were carried out. Lead discs were used as the work material. The cutting speed was 0.2 mm/s. The wear land of various widths on the tool flank face was simulated by grinding the corresponding lands with a zero flank angle.

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

181

tc−f

sc−f

(MPa)

t1 = 0.55 mm

(MPa)

t1 = 0.15 mm

s

t1 = 0.10 mm

12

8

8

4

(a) t

4

0

0 0

0.2

0.4

0.6

0.8 x (mm)

tc−f (MPa) 8

t1 = 1 mm

sc−f

4

(MPa) t1 = 2 mm

8

(b)

t1 = 1 mm

4

0

0

t1 = 2 mm 0

0.2

0.4

0.6

0.8

x /hf

Fig. 3.43. Normal and shear stress distributions at the tool–workpiece interface in machining of lead at ν = 0.2 mm/s, dw = 3 mm: (a) in turning with different uncut chip thicknesses (t1 ), x is the distance from the cutting edge, (b) in shaping with two different widths of the lank on the flank contact surface (hf ).

The distributions of the normal and shear stresses obtained in the turning test with three different uncut chip thicknesses are shown in Fig. 3.43(a). As seen, both stresses gradually decrease with increasing distance from the cutting edge and abruptly decrease in the vicinity of the end of the modeled land. A comparison of the experimentally obtained distributions with those obtained in the modeling of punch penetration discussed earlier shows their similarity although the distribution of the normal stress on the flank face differs from that on the rake face by the presence of an abrupt segment at the end of the land.

182

Tribology of Metal Cutting

The distribution of the normal stress at the end of contact (Fig. 3.43(a)) shows that there is no increase in the contact stress in the vicinity of this end as might be expected. For this kind, the end condition is similar to that for a punch having sharp corners (Figs. 3.7(a) and (b)). This, however, can be readily explained by the curvature of the workpiece. This curvature “weakens” the contact in the vicinity of point E (Fig. 3.42(b)) that, in turn, lowers the contact stresses at the end of the contact. The wider the width of the wear land, the smaller is the diameter of the workpiece and the weaker is the contact at point E. The distributions shown in Fig. 3.43(b) obtained in orthogonal cutting (shaping), where the machined surface is flat, confirm this point. As seen, the stress distribution in this case is more uniform and the distinctive stress maxima are observed in the vicinity of point E. Increasing the width of the flank land results in the smoothing of the maxima in the vicinity of point E, while the maxima at the cutting edge end remain sharp. The analysis of the distribution of the stress on the tool–workpiece interface results in the following conclusions: • The distribution of the shear stress over the tool–workpiece interface does not have the same flat region as the shear stress distribution over the tool–chip interface does over the plastic part of the tool–chip contact (adjacent to the cutting edge). It suggests that there is no or little small plastic contact zone at the tool–workpiece interface. • The ratio of the shear and normal stresses at the region adjacent to the cutting edge (which could be thought of as the apparent friction coefficient) reaches 1 or even higher. In this respect, it is similar to that found at the elastic part of the tool–chip interface. This creates conditions for adhesion to occur at this interface. • Over the rest of the tool–workpiece contact length, the ratio of the shear and normal stresses stabilizes approaching 0.5–0.7. In this respect, the tribological process at the tool–workpiece interface is closer to the classical hard pin-on-soft disc case than that at the tool–chip interface. A good coincidence of the normal and shear stresses distributions obtained for various uncut chip thickness (Fig. 3.43) is an important experimental result. This is the first experimental evidence that the stresses at the tool–workpiece interface do not depend on the uncut chip thickness. Experiments also showed that the stress distribution curves do not change with the rake angle while the mean contact stresses do. For example, an increase in the rake angle leads to a decrease in the mean contact stresses at this interface. The introduction of the cutting fluid at the tool–workpiece interface reduces the mean shear contact stresses while the mean normal contact stress is not affected. The shape of the stress distribution curve does not change in this case either. In parallel with the discussed photoelastic tests, the actual cutting force has been measured and the total forces acting on the tool flank were determined as the force intercept at zero uncut chip thickness. In these tests, the vertical (Fz ) and radial (Fy ) components

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

183

Table 3.2. Comparison of normal and shear forces at the tool–workpiece interface found using various experimental methods. Cutting conditions

Rake angle

Forces at the tool–workpiece interface FfN

Dry With the cutting fluid (kerosene)

0 15 0 15

FfF

Photo elasticity

Extrapolation

Photo elasticity

Extrapolation

15.6 12.1 13.9 12.9

14.5 12.0 13.0 11.5

16.2 12.9 12.0 9.5

16.0 13.5 11.0 8.5

of the resultant cutting force have been measured using a dynamometer. Then the normal (FfN ) and shear (FfF ) forces acting at the tool–workpiece interface have been determined. Table 3.2 shows these forces in comparison with those obtained using the method of photoelasticity. A fairly good agreement of the normal and shear forces at the tool–workpiece interface obtained using these two methods confirms the validity of the force intercept at zero uncut chip thickness method. The stresses at the tool–workpiece interface are parts of the general state of stress in the formation zone. Because the angle of action, ωac (Fig. 3.8) is directly determined by the work in the plastic deformation of the work material, there should be direct correlation between CCR, ζ and FfN . Moreover, this correlation should be more vivid for a small flank wear land. Zorev pointed out [2] that there is a correlation between CCR and FfN . He explained it by the correlation between CCR and the workhardening of the work material. As such, the correlation between ζ and FfN should be stronger for work materials with a greater ability for workhardening. Poletica argued [69] that if it is so, the correlation between ζ and FfN due to workhardening of the work material should be the same for the entire length of the tool–workpiece interface while the correlation between ζ and FfN due to the field of stress around the cutting edge shows up at this interface in the vicinity of the cutting edge. To clarify the issue, the study of the correlation between ζ and FfN was conducted for a wide range of work materials and cutting conditions [69]. The cutting tests were carried out using “sharp” tools having no significant flank contact land. To accomplish this, the cutting tool edge preparation was used before each run and the test time did not exceed several minutes. This time was more than sufficient to reach thermal balance in the cutting system. The wear land after the test did not exceed 0.05–0.07 mm even for the hardest work materials. Figure 3.44(a) shows a typical correlation of the flank forces FfN , FfF and CCR ζ for ductile materials. As seen, both forces increase with ζ. When CCR is small, the shear force FfF is less than the normal force, FfN so the apparent friction coefficient is less than 1. When ζ increases, the shear force FfF increases becoming first equal to and then greater than the normal force FfN , so the apparent friction coefficient exceeds 1.

184

Tribology of Metal Cutting F(N) FfN 200

(a)

FfF 100

6

10

8

12

ζ

14

F(N ) FfN

FfN

FfN

200 FfF

(b)

FfF

100

HB110 HB220 HB320

FfF

2

4

6

z

Fig. 3.44. Correlations between CCR and forces on the tool flank: (a) for copper, rake angle γ = 10◦ , tool cutting edge angle κr = 70◦ and depth of cut dw = 3 mm, (b) beryllium copper of different hardness, rake angle γ = 10◦ , tool cutting edge angle κr = 70◦ and depth of cut dw = 2 mm.

This can only be explained by the corresponding increase in the stress in the vicinity of the cutting edge. In other words, the zone of the work material brought to the plastic state in the vicinity of the cutting edge increases. This leads to the condition where the greater part of the flank land is in contact with the work material brought to the plastic state. When the hardness of the work material increases, the ratio of the shear and normal stresses (the apparent friction coefficient) decreases although both forces FN1 and Ff 1 grow (Fig. 3.44(b)). Each hardened state of beryllium copper yields in the group of experimental points shifted along the ζ axis. Compiling these data, Poletica concluded [69] that there is a correlation between the apparent friction coefficient at the tool– workpiece interface and CCR. Figure 3.45 shows the experimentally obtained normal and shear forces on the tool flank surface as functions of CCR for a wide variety of work–tool material combinations. The increase in the tendency of force with the hardness of the work material is especially noticeable for the normal force (FfN ). The greater the hardness, the higher is the location of the corresponding curve FfN = f(ζ).

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

185

FfF (N ) 600

3 1

6

2 5

400

10

11

4

200

13

9 12

8

7

0 0

4

8

12

16

20

z

20

z

FfF (N ) 6 600

11

10 400

2 1

200

4

5

3

9 8

7

0 0

12

4

13 8

12

16

Fig. 3.45. Correlations between CCR and forces on the tool flank for various combination of the work and tool materials: 1 – beryllium copper HB320-carbide M30, 2 – beryllium copper HB200carbide M30, 3 – steel 07-carbide P20, 4 – Ti Grade 1-carbide M10, 5 – steel A514-carbide P20, 6 – Armco iron-carbide P20, 7 – cadmium-HSS M42, 8 – Lead-HSS M42, 9 – Al 2014-HSS M42, 10 – beryllium copper HB110-carbide M30, 11 – copper -Ti Grade 1, 12 – HSS M42 and 13 – Al-HSS M42.

It is important to note that for three materials having similar mechanical properties characterized by their hardness (steel 07, beryllium bronze tempered to HB200 and Ti Grade 1), the experimentally obtained relationships FfN = f(ζ) are very close. At the same time, the chip-formation and tribological parameters at the tool–chip interface as the contact length, CCR, apparent friction coefficient, etc. are considerably different (Figs. 3.16, 3.25, 3.26, etc.). Similarity methods. To estimate the forces acting on the tool flank and contact stresses, consider the model shown in Fig. 3.46. According to this model, the cutting tool has the cutting edge radius, ρce . Due to this radius, the total uncut chip thickness (t1 ) is separated into the actual uncut chip thickness (ta ) and the layer of thickness (h1 ) to be burnished by the round part adjacent to the tool flank face. The arc distance between points A and D is designated as ∆ and is given by ∆ = (∪AC) + (∪CD) = ρ1 ψ +

her , sin α

(3.67)

186

Tribology of Metal Cutting

Chip Tool

B E

h1

Workpiece

rce

a

F

A

D her

t1

ta

y j

C ∆

D1

Fig. 3.46. Model of the chip–workpiece interface.

where ψ is the central angle corresponding to arc AC and her is the elastic recovery of the machined surface. Because ψ = arccos (1 − h1 /ρce ), then ψ = arccos (1 – hp /ρ1 ) and  ∆ = ρ1

   h1 her arccos 1 − + ρce ρce sin α

(3.68)

It is known [68] that the cutting process ceases and the layer to be removed undergoes plastic deformation similar to burnishing when τin h1 ≤ 0.5 − , ρce σYT

(3.69)

where σYT is the yield strength of the work material, τin is the strength of adhesion bonds at the tool–workpiece interface determined using results of the adhesion tests [82]. As discussed above, the strength of the adhesion bonds depends on the mutual adhesion properties of the tool and work materials. Substituting Eq. (3.69) into Eq. (3.68), one can obtain

 her 0.5 − τin  σ τin ∆ YT + = arccos 0.5 + σYT ρce h1 sin α

(3.70)

The plastic deformation of the surface layer can be characterized by the burnishing factor m = h1 / her which according to Poletica [69] can be approximated by CCR. As a result,

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

187

Eq. (3.70) becomes    (0.5 − τin /σYT ) sin ϕ ∆ τin Br + = arccos 0.5 + ≈ 1.25 , ρce σYT cos (ϕ − γ) sin α sin α

(3.71)

where Br is a similarity criterion, referred to as the Briks criterion [36,68], Br =

cos γ ζ − sin γ

(3.72)

The experimental results showed that h1 ≈ 0.5ρce is a good approximation when cutting ductile materials [68]. As such Eq. (3.71) becomes  ∆ = ρce

π 0.5 sin ϕ + 3 cos (ϕ − γ) sin α

 (3.73)

As it follows from Eqs. (3.71) and (3.73), the contact length on the tool flank is a function of the tool rake angle and CCR. Using the above considerations and the model shown in Fig. 3.46, one can obtain expressions for h1 and her as  h1 = ρce 1 − 

her =

1



1 + Br 2

(3.74)



 ρce 1 − 1/1 + Br 2 Br cos γ + Br sin γ

(3.75)

According to Poletica [69], the stress distribution at the flank contact surface is as follows   x 2 τc−f (x) = τy exp −3 , ∆

(3.76)

where τy is the yield shear strength of the work material and x is the distance from the cutting edge. Integrating Eq. (3.76) yields the mean shear stress at the tool–flank interface τc−f = 0.505τy

(3.77)

188

Tribology of Metal Cutting

which is in excellent agreement with the experimental result obtained by Zorev [2] and Chen and Pun [83]. Knowing the mean shear stress, one can calculate the mean normal stress as σaf =

0.505τy , µff

(3.78)

where µff is the apparent friction coefficient on the tool–flank contact area. Figures 3.43–3.45 allow to obtain this friction coefficient for various combinations of the work and tool materials because this friction force is calculated as the ratio of the shear and normal stresses at the tool–workpiece interface. Bearing in mind Eq. (3.77), one can obtain the expression for friction force at the tool flank as  Br FfF = τc−f lce−a ∆ = 0.505τy b1 ∆ = 0.625τy ρce b1 , (3.79) sin α where b1 is the width of cut which calculates depending on the tool geometry as discussed in Appendix A. The normal force at the tool–flank interface is then calculated as  FfF 0.625τy ρce b1 Br FfN = = µff µff sin α

(3.80)

3.3.3 Generalizations The results of the theoretical and experimental studies on the tribological conditions at the tool–workpiece interface can be summarized as follows: • The distribution of the normal and shear stresses have maxima in the region adjacent to the cutting edge. Then the level of stresses stabilizes over the contact length becoming zero at the end of the contact. The smaller the curvature of the workpiece surface, the higher is the level of contact stresses at the end of the contact, where both stresses may have second maxima. • There is no or very small region of the plastic part of the interface. • Adhesion takes place in the region adjacent to the cutting edge while simple friction is the case on the rest of the interface. • The normal and shear stresses depend on the mechanical properties of the work material (primarily on its hardness), while other material characteristics, including material type, do not seem to have any noticeable effect. • The stresses at the interface strongly correlate with the processes in the deformation zone and tool geometry through CCR and Br.

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189

• Although the level of stress, temperatures and strength of adhesion bonds are much weaker at the tool–workpiece interface compared to those at the tool–chip interface, the sliding velocity at the tool–workpiece interface is much higher (by CCR). The more ductile or difficult-to-machine material, the higher is the difference in the sliding velocity. This explains why flank wear is often greater than that on the tool rake face in machining these types of the work material.

3.4 Temperature at the interfaces 3.4.1 Temperatures significant to the tribology of metal cutting Although it is pointed out in almost any book on metal cutting that temperature, and particularly, its distribution has a great influence in machining [60], no one study known to the author quantifies this influence. Instead, it is stated in very general and qualitative terms that temperatures in metal cutting affect “the shear properties” of the work material and, therefore, they affect the chip-forming process itself, and through their effect on the tool, they determine the limits of the process and mode of tool wear. To address each of these points, a great number of works on temperatures in metal cutting have been published. Apart from many contradictive results that can be readily found in the published works and can be logically explained by the difference in the experimental methodologies and accuracy of calibration, numerical and analytical models and the assumptions adopted in both the models, the major concern with these works is their practical significance. In other words, there is no answer to a simple question: “What should one do with the found temperature and its distribution?” Trent and Wright concluded [37] that the major objective of heat consideration in metal cutting is to explain the role of heat in limiting the rate of metal removal when cutting the higher melting point metals. They concluded that there is no direct relationship between cutting forces or power consumptions and the temperature near the cutting edge. Zorev [2] did not consider temperature as an important factor itself. Considering the energy balance in metal cutting, he calculated that the maximum temperature at the end of the chip formation zone does not exceed 270◦ C for plain and alloyed steels while a considerable reduction in the mechanical properties of these material starts only at temperatures over 300◦ C. According to Childs et al. [58], the two goals of temperature measurements in machining are: (a) the quantitative measurements of the temperature distribution over the cutting region is more ambitious, but very difficult to achieve, and (b) is less ambitious to measure the average temperature at the tool–chip contact. Although the authors presented short description of various methods of temperature measurements in metal cutting, they did present results of such measurements and their use in the considerations of tool wear and other outcomes of the machining process. Altintas [84] did not consider temperature to be a factor not only in the cutting mechanics but also in his consideration of dynamic stability and structural errors of the machining system.

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Gorczyca in his book attempted to show the practical application of metal cutting theory [56]. Unfortunately, he presented only the qualitative influence of temperature. He operated with the so-called burnout temperature and cutting temperature. The burnout temperature is defined as that temperature “at which the tool cannot efficiently perform the cutting process.” Unfortunately, this characteristic is not listed in any specification of tool materials. Shaw in his book [34] presented a very detailed description of various methods of temperature assessment in metal cutting. He pointed out that there are several temperatures of importance in metal cutting: • The shear plane temperature because it may, in his opinion, influence on the flow shear stress of the work material and also has a major influence on the temperature of the tool face and on that of the tool flank. • The temperatures on the tool face and flank are very important to crater wear rate and rate of wear-land development on the tool flank surface. The temperature on the tool face also plays a major role relative to the size and stability of the built-up edge. • The ambient temperature of the workpiece is also important because it directly affects the above three listed temperatures. A simple critical analysis of the temperatures listed by Shaw shows that the temperature of the shear plane cannot play the role assigned by Shaw. First of all, it does not affect the flow shear stress of the work material as conclusively proven by Zorev’s calculations based on the experimental results [2] and by Astakhov using direct comparison of cutting and compression [36]. Second, the temperature at the upper boundary of the deformation zone (that is the shear plane in the terminology used by Shaw) cannot significantly affect the temperatures at the interfaces. This is because the shear plane temperature does not exceed 200◦ C while the temperatures on the tool–chip and tool–workpiece interfaces are 3–6 folds higher. As others, Shaw did not consider the use of the temperature data in metal cutting consideration as for example in the assessment of tool wear. Oxley [35] considered some temperature calculations in the relation of temperature rise in the deformation zone and its possible influence on the mechanical properties of the work material in terms of reduction of the flow shear stress. In his consideration of tool life, Oxley came to a conclusion that the temperature of the tool flank should be considered in the tool life calculation. According to Oxley, this average tool flank temperature is 11% lower than that at the tool–chip interface, although the practice of machining and other available information on the matter do not support this statement. In the author’s opinion, a confusion with temperatures in machining and their proper applications to the assessment of the process output parameters stems from nontribological considerations, where the temperature considered alone without other tribological conditions at the interfaces has very little significance, particularly when it is considered apart from the energy balance of the cutting system discussed in Chapter 2.

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191

The analysis of the energy balance in metal cutting (Chapter 2), heat sources and heat partition in the metal cutting system [36], results of similarity studies of the metal cutting process [36,68], and physical aspects of tool wear and tool resource [77,85–87] allowed to list temperatures that are most relevant in metal cutting tribology: • The average integral contact temperature as measured by the tool–work thermocouple technique. As shown by the practice of metal cutting research [68,85,88,89], this is the most stable and relevant characteristic that can be measured with high accuracy, great repeatability and reproducibility. The importance of this temperature is that this is the only temperature that can be reliably correlated with tool life and to be used in the optimization of the cutting process, as discussed in Chapter 4. Hereafter, this temperature is referred to as the cutting temperature. • The maximum contact temperature. This temperature is of great interest for the developers of various tool materials as this maximum temperature should not cause the plastic lowering of the cutting edge (discussed in Chapter 4) or catastrophic tool failure. The location of the region of maximum contact (normally occurs at the tool–chip interface) temperature with respect to the cutting edge is also of some methodological interest.

3.4.2 Assessment of temperatures in metal cutting There are four basic methods in the assessment of temperature in metal cutting, namely, analytical, numerical, similarity and experimental. Analytical and numerical methods. There were a great number of various attempts to assess the temperature and its distribution in metal cutting using various analytical (well summarized by Shaw [34], Reznikov [90] and Komanduri [91–93]) and numerical methods as FEA [94–97] and boundary elements [98] methods. Regardless of the great diversity of these methods, the following drawbacks make their results of little help in the consideration of the tribological aspects in metal cutting: • They cannot predict in principle the cutting temperature (in the sense of the definition given above in Section 3.4.1). • They are based on the single-shear plane model with severe drawbacks as discussed in Chapter 1. • They did not account for the significant part of energy spent in the deformation zone as pointed out by Atkins [99,100]. • None of the models used in the analytical and numerical simulations accounts for the real contact stresses at the tool–chip and tool–workpiece interfaces. • Numerical methods based on the FEA analysis suffer severe errors when applied to analyze great plastic deformations. To account for these deformations, dimensional change cause a complete restructuring of the resulting mesh and the error due to remeshing would overshadow the changes in the solution.

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The following assumptions are common in the known analytical and numerical modeling of metal cutting: • The tool is ideally sharp and unworn. • The chip formation process is continuous without plastic zone attached to the tool rake face (known as the built-up edge). • The chip moves as a rigid body relative to the tool. • Heat flow is steady in the cutting tool and quasi-steady in the chip and the workpiece. • The deformation of the chip in the shear plane is uniform, so the heat generation is uniform over the chip cross section. • The temperature of the chip is uniform as it leaves the shear zone. • When modeling the chip heating at the tool–chip interface, the chip is viewed as a semi-infinite solid when modeling the moving heat source effect at this interface. Likewise, the workpiece is also viewed as a quarter-infinite solid when modeling the stationary heat source effect at the tool–chip interface. • When modeling the tool heating at the tool–chip interface, the dimensions of the cutting wedge are sufficiently large, so it can be represented as a quarterinfinite solid when modeling the stationary heat source effect at the tool–chip interface. • Heat losses due to convection and radiation for all surfaces of the chip, workpiece and tool are negligibly small. Naturally, such assumptions make the modeling unrealistic. Although the results of analytical and numerical modeling cannot be used today in tribological analyses of the metal cutting process, their further developments should not be discouraged. The problem is in using the correct physical model and its boundary conditions. In FEA method, the emerging meshless methods (LS Dyna) look very promising for numerical analysis in metal cutting. Similarity methods. Similarity methods are much less sensitive to the particular model used in modeling particularly when applied to the thermal analysis of metal cutting [36,68]. The results of similarity analysis allow calculating the maximum temperature at the interfaces as well as the cutting temperature. The temperature of the tool rake face at point O (Fig. 3.21) can be estimated using the energy balance approach. The energy EO−t released in the vicinity of this point can be thought of as the sum of the energy of plastic deformation (EO−pd ) (Eq. (2.24)) and energy required for the formation of new surfaces (EO−ns ) [101], i.e. EO−t = EO−pd + EO−ns = Au νt 1 dw1 + EO−ns

(3.81)

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193

On the other hand, the thermal energy generated in this region can be represented as given in Ref. [68] QOA

  t1 dw1 Cp ρ w θO = ,  erf PeBr 4

(3.82)

where Br is the Briks criterion (Eq. 3.72), Pe is the Péclet criterion (Chapter 2, Section, Péclet Criterion Eq. (2.35)), erf (z) is the “error function” encountered in integrating the normal   distribution (which is a normalized form of the Gaussian function) [102,103] and Cp ρ w is the specific heat of the work material. Thus, energy balance EO−t = QOA yields in the expression for the maximum temperature at point O  θO =

  PeBr Au + (EO−ns /νt1 dw1 )   erf 4 Cp ρ w

(3.83)

Analysis of Eq. (3.83) shows that the maximum temperature at point O is determined by the mechanical and thermal properties of the work material as well as by the parameters of the machining regime. As the cutting speed and uncut chip thickness√increase (Pe = νt1 /ww as per Eq. (2.35)), product PeBr increases. When PeBr ≥ 20, erf (PeBr/4) = 1 and the expression for the maximum temperature at point O simplifies to θO =

Au + (EO−ns /νt 1 dw1 )   Cp ρ w

(3.84)

In this equation, Au is calculated using CCR (Eq. (2.24)) and EO−ns is calculated using the data presented by Atkins [101]. Calculations, however, showed that in a wide range of Pe when PeBr ≥ 20, this temperature becomes invariant to the cutting parameters and can be considered as a characteristic of the work material. For the limiting stabilized cutting regime, the maximum temperature at point O is determined as θO = nθ Tm

(3.85)

where nθ is a proportionality coefficient. For all metallic work materials nθ = 0.25 and Tm is the melting temperature of the work material (Table 3.3). The maximum temperature at the tool flank, θfl−max occurs in the middle of the tool– workpiece interface. This temperature is calculated as  θfl−max = θO

 0.36 sin0.25 α 0.5 + 1.25  + ψN , Br PeE ρ

(3.86)

where Eρ is the relative sharpness similarity criterion, Eρ =

ρce t1

(3.87)

194

Tribology of Metal Cutting Table 3.3. Melting points of some work materials. Material

Symbol

Melting point (◦ C)

Aluminum Brass (85 Cu, 15 Zn) Bronze (90 Cu, 10 Sn) Cast iron Chromium Copper Inconel Iron Lead Magnesium Manganese Monel Nickel Silicon Stainless steel High-carbon steel Medium-carbon steel Low-carbon steel Tin Titanium Tungsten Zinc

Al Cu+Zn Cu+Sn C+Si+Mn+Fe Cr Cu Ni+Cr+Fe Fe Pb Mg Mn Ni+Cu+Si Ni Si Cr+Ni+Mn+C Cr+Ni+Mn+C Cr+Ni+Mn+C Cr+Ni+Mn+C Sn Ti W Zn

659 900–940 850–1000 1260 1615 1083 1393 1530 327 670 1260 1301 1452 1420 1363 1353 1427 1464 232 1795 3000 419

and  0.6nα−θ B1.25 PeEρ cos α ψN =  sin0.25 α × erf PeBr 4

(3.88)

where 

nα−θ = 1+

1 0.1 0.3 0.24F √ θ D 0.2 sin α PeEρ Br 01

,

(3.89)

where Fθ is the similarity criterion that accounts for the thermal properties of the tool and work materials as well as for the tool geometry Fθ =

kt βn εκ , kw

(3.90)

where kt and kw are the thermal conductivities of the tool and work materials, (J/(m × s × K)), βn is the cutting wedge angle in the normal plane (rad) (Appendix A), εκ is the angle between the major and the minor cutting edge in the reference plane (rad)

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

195

that calculates through the tool cutting edge angles of the major (κr ) and minor (κr1 ) cutting edges (Appendix A) as εκ = π − (κr + κr1 )

(3.91)

D is the similarity criterion that accounts for the parameters of the uncut chip thickness (Appendix A) D=

t1 lce−a

(3.92)


As before, lce−a is the active length of the cutting edge. Normally, lce−a = dw sin κr . The distribution of temperature over the contact length ∆ (Fig. 3.46) is defined as (the x2 axis is perpendicular to the cutting edge) ⎛ ⎜ θfl (x2 ) = θO ⎝0.5 + 0.25

0.25

sin 

Br 1.25

α

PeE ρ x∆2

 + 2.12ψN

x2 ∆

⎞  2 x2 ⎟ 1− ⎠ 3∆



(3.93)

The second additive in brackets in Eq. (3.93) is a decreasing function within 0 ≤ x2 /∆ ≤ 1 while the third additive is a function having its maximum at x2 /∆ = 0.5. Therefore, the maximum contact temperature at the tool–chip interface is in the range of 0 ≤ x2 /∆ ≤ 0.5. The exact location of the point of maximum is found by differentiating Eq. (3.93) and setting the differential to zero. The obtained result is  x

2

∆

max

= 0.25 +

!

0.0635 −

0.1 sin0.5 erf



PeBr 4

nα−θ PeEρ Br 2.5 cos α

(3.94)

Analysis of Eq. (3.94) shows that with increasing the cutting speed (Pe), the second term under the square root decreases which leads to increasing (x2 /∆)max . This second term is equal to zero in the limit, so the maximum (x2 /∆)max = 0.5. Conversely, when the cutting speed decreases, the maximum temperature on the tool–workpiece   interface shifts towards the cutting edge. In the limit,

PeBr 4 2.5 nα−θ PeE ρ Br cos α

0.1 sin0.5 erf

= 0.0625 so

that the minimum (x2 /∆)max = 0.25. Therefore, for a wide range of practical machining conditions, 0.25 ≤ (x2 /∆)max ≤ 0.5. Analysis of Eq. (3.94) also shows that the higher the thermoconductivities of the tool and work materials and the smaller the radius of the cutting edge, the smaller is (x2 /∆)max , i.e. the closer is the point of the maximum temperature to the cutting edge.

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Tribology of Metal Cutting

qfl /qO

qfr /qO

2.0

3.5

1.8

3.0

1.6

2.5

1.4

2.0

1.2

1.5

1.0

1.0 0

0.2

0.4

0.6

0

0.8 x2 /∆

0.25

(a)

0.50

0.75

1.00

1.25 x2 /Ic

(b)

Fig. 3.47. Temperature distributions: (a) over the tool–flank interface, ψN = 1.415, Pe = 35, Br = 0.715 and α = 10◦ , (b) over the tool–chip interface, ψM = 2.0.

An example of the calculations of the temperature distribution over the tool–workpiece interface using Eq. (3.93) is shown in Fig. 3.47(a). The distribution of temperature over the tool rake face can be calculated as (the x1 axis is perpendicular to the cutting edge): 



θfr (x1 ) = θO 1 + ψM 



θfr (x1 ) = θO 1 + ψM

x1 lc /2 lc /2 x1

 ,

when

0 ≤ x1 ≤ lc /2,

(3.95)

when

x1 > lc /2,

(3.96)

0.6  ,

where

ψM

" √ 0.9675nγ−θ PeBr cos γ + sin γ − Br (cos γ − sin γ) =  cos γ + Br sin γ erf PeBr 4

(3.97)

and nλ−θ =  1+

1 √ 0.3

0.25FD sin γ+Br cos γ   √ 0.3 PeBr cos γ+sin γ−Br(cos γ−sin γ)0.2



(3.98)

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197

The maximum temperature at the tool rake face θfr−max is calculated as θfr−max = θO (1 + ψM )

(3.99)

The temperature at point C (Fig. 3.21(a)) where the chip separates with the tool rake face is calculated as θfr−C = θO (1 + 0.66ψM )

(3.100)

An example of the calculations of the temperature distribution over the tool rake face is shown in Fig. 3.47(b). The cutting temperature in the sense of definition is given in Section 3.4.1 and is calculated as ⎛ ⎞  0.375 E0.055 erf 0.4 PeBr 0.95τ Pe c 4 ⎜ ⎟ θ=⎝ (3.101) 0.65 0.03 ⎠ 0.15 0.625 0.045 (1 − sin γ) Cp−w ρw Br Fθ D sin α Analysis of Eq. (3.101) arrives at the following conclusions: • As the cutting speed (ν) and uncut chip thickness (t1 ) increase (so does Pe = νt1 /ww as per Eq. (2.35)), the cutting temperature increases. As such, t1 has a smaller influence as it is found in numbers E and D. • The cutting temperature grows with the strength of the work material. However, its power is less than 1 because it affects CCR and thus Br. • With  increasing the thermoconductivity (kw ) and specific heat of the work material Cp ρ w and thermoconductivity of the tool material (kct ) the cutting tempera ture decreases. If it is assumed that Br and erf 0.4 PeBr 4 remain unchanged, then Eq. (3.101) can be represented in the following form θ=

cθ  0.15

kw0.225 kct

Cp ρ

0.625 ,

(3.102)

w

where cθ is a constant. • The depth of cut, dw affects the cutting temperature through the active length of the cutting edge, lce−a (lce−a = dw /sin κr ) and the uncut chip thickness, t1 . It increases the cutting temperature at a power of 0.045. • The cutting edge radius increases the cutting temperature at a power of 0.055 while working with a tool having no wear. • The other parameters of the tool geometry affect the cutting temperature directly, as the rake angle γ and flank angle α (see Eq. (3.101)) or indirectly through F and Br numbers.

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Tribology of Metal Cutting q

q /qO q /qO

1200

7 q

1000

6

800

5

600

4

400

3 qO

200

2

0

1 0

20

40

60

80

100

120

140 Pe

Fig. 3.48. Dependence of the cutting temperature θ, temperature at point O (θO ) and their ratio on the Piéclet criterion (Pe).

The dependences of θO , θ and their ratio θ/θO on the Péclet criterion, Pe in turning steel AISI 1045 using P20 (15% TiC, 6%  Co,  79% WC) are shown  in Fig.  3.48 for the following conditions: τc = 485 × 106 Pa, Cp ρ w = 5.02 × 106 J/ m3◦ C , ww = 8 × 10−6 m2 /s, kw = 40.2 J/(m · s ·◦ C), kt = 27.2 J/(m · s ·◦ C), γ = 10◦ , α = 10◦ , κr = 45◦ , κr1 = 15◦ , ρce = 0.01 × 10−3 m, rn = 1 × 10−3 m, f = 0.2 × 10−3 m, dw = 2 × 10−3 m, t1 = 0.141 × 10−3 m, lce−a = 2.88 × 10−3 m, Fθ = 1.75, Eρ = 0.71, D = 0.05. Values of Pe and Br used in calculations are shown in Table 3.4. The results of the calculations and analysis of Fig. 3.48 show that although the cutting speed is very high, the maximum temperature at point O in machining steel AISI 1045 is relatively low falling in the range between 82 and 185◦ C. When Pe = 20, this temperature has its maximum θO = 185◦ C and then it reduces assuming practically a constant value

Table 3.4. Pe and Br as functions of the cutting speed. ν (m/s)

Pe

Br

0.062 0.123 0.237 0.493 0.950 1.9 3.93 6.17 8.85

1.1 2.2 4.2 8.6 16.7 33.5 70.0 109.0 156.0

0.452 0.573 0.562 0.562 0.502 0.532 0.573 0.641 0.641

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199

of θO = 151◦ C. The cutting temperature increases with the cutting speed, ν(Pe) from 130 to 1240◦ C and thus the ratio θ/θA increases from 1.6 to 8.2. The foregoing analysis suggests that the similarity method is simple and straightforward compared to the other methods of temperature determination. In the author’s opinion, this method should be used instead of bulky analytical and inaccurate numerical methods in the simulation software packages. Experimental methods. The great difficulties in predicting temperatures at the interfaces even for very simple conditions led to the development of a number of experimental techniques to measure temperatures in metal cutting. These can be broadly divided into two categories as non-contact and contact methods. Among non-contact methods, microstructural (metallurgical) method and infrared thermography are predominant nowadays. Among the contact methods, temperature measurement using thermocouples is the most common. Microstructural methods. These are based on the correlation between temperature and the microhardness and metallurgical structure of the workpiece or the tool materials and the temperature. Normally [104–106], the correlation between microhardness and maximum temperature that occur during cutting is used to determine the temperature distribution in tools made of high speed steel. There are two drawbacks of this method: • The accuracy is low reaching at best ±25% [105]. • It can be applied only for certain types of tool materials such as high speed steels. It is not applicable for carbide, PCD and ceramic-based tool materials used nowadays. Other examples of metallurgical methods are the use of powders [107] or physical vapor deposition (PVD) coatings [108] applied on a section of split tool or split workpiece, and chemical element substitution in the tool [109,110]. Knowing the melting point of the introduced alloys, it is possible to reconstruct the temperature field by drawing isothermals on the scaled drawing of the tool or workpiece section after cutting and by metallographic analysis. This method, however, suffers severe drawbacks as: • Any material melts when its temperature reaches the melting point and is allowed to stay at this temperature for sometime. Basically, there are two types of transformation diagram that determine this time, namely, time–temperature transformation (TTT) and continuous cooling transformation (CCT) diagrams. Time–temperature transformation diagrams measure the rate of transformation at a constant temperature. In other words, a sample is austenitized and then cooled rapidly to a lower temperature and held at that temperature whilst the rate of transformation is measured, for example, by dilatometry. Continuous cooling transformation diagrams measure the extent of transformation as a function of time for a continuously decreasing temperature. In other words, a sample is austenitized and then cooled at a predetermined rate and the degree of transformation is measured, for example, by dilatometry. A simple analysis of these diagrams for common work materials shows that there is not sufficient heating time available in metal cutting and the rate of cooling is not known. As shown by Astakhov (p. 138 in [36]), at a

200

Tribology of Metal Cutting typical cutting regime, a microvolume of the work material is exposed to high temperatures during the time period of 0.000014–0.00075 s that might not be sufficient for melting even if the temperature of this microvolume reaches the melting point.

• When using various coatings on the tool and workpiece, a concern is that these coatings change the thermal properties of the tool and work material. For example, Outeiro, Dias and Lebrun reported [111] that a coating applied on the tool dramatically changes the temperature distribution in the metal cutting system. • Because this test is of a post-process nature, it is not possible to correlate the obtained result with the time frame of the cutting process. Infrared thermography. Infrared, infrared thermography, thermal imaging, infrared radiometry, infrared imaging, and IR condition monitoring are all terms used in this growing field of temperature measurements. No matter which particular term is used, infrared radiometrics and thermal imaging have a wide diversity of applications. The technique allows for the monitoring of temperatures and thermal patterns while the equipment is online and running under full load. It is increasingly used as an emerging experimental technique in metal cutting for various temperature measurements. The major advantage of infrared thermography is that it does not interfere with the cutting process. Photography cameras with infrared-sensitive films [112–114], optical pyrometers [115–119] and the infrared cameras [120–125] are typical apparatus that are used to detect the infrared radiation from a zone of high temperature. Infrared cameras are the most suitable for the determination of the temperature distribution in the deformation zone [111]. Different infrared cameras have applications in metal cutting studies, from the classical infrared scanning cameras with only one sensor [120] to the most advanced infrared cameras having a detector with an array of sensors, as is the case of the FPA (Focal Plane Array) infrared detector [121,122]. The latter design allows for more accurate measurements when strong temperature gradients occur as those in metal cutting systems. Figure 3.49 shows a schematic of a typical measuring setup used in infrared thermography [111]. It includes a charge-coupled device (CCD) camera, objective, high-pass filter, a pair of lenses of the convergent type and a graduated rail, where these listed components were mounted. This assembly is then installed on a machine tool. In addition, cooling and control units and a computer with dedicated data acquisition hardware and software are connected to the CCD camera. The CCD camera is normally a gray-level digital camera equipped with a special CCD detector, which presents high sensitivity, low noise and high resolution. This camera is capable to work both in the visible and in the near infrared regions (up to 1000 nm). The operating parameters of the CCD camera, such as the exposition time of the CCD and the CCD temperature are set and controlled by the control unit. To analyze only the infrared radiation emitted by one object, the visible radiation should be illuminated using for example a high-pass filter (or infrared filter). Outeiro, Dias and Lebrun recommended [111] a filter that eliminates the radiation below 850 nm.

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

201

Fig. 3.49. Schematic representation of the thermal imaging setup (Courtesy of J.C. Outeiro).

Such a filter is mounted directly into the objective of the camera. Therefore, the CCD only receives radiation in a wavelength range between 850 and 1000 nm. To analyze precisely the temperatures in the deformation zone, the size of the temperature field analyzed by the camera should be of the order of a few millimetres, and this area should be sufficient to cover the zone around the tool tip. The desired area (spatial resolution) for temperature measurements is achieved, using, for example, a pair of magnifying lenses placed between the camera and the machining zone. Because the precise adjustment of the focal distance of the two lenses is needed, the camera is mounted on the same graduated rail as the lenses. To obtain a fixed spatial resolution during temperature measurements, the camera must follow the motion of the objects under analysis, so, it should follow the feed motion of the tool. Therefore, the assembly that includes the CCD camera, objective, infrared filter, pair of convergent lenses and a graduated rail must be installed on the carriage that has the feed motion. To analyze the temperatures in the zone around the tool tip at different angles with respect to the tool reference plane, a special structural support is to be used. Such a support allows changing the orientation of the rail, and thus the camera. Normally, temperatures are analyzed in the zone around the tool tip in the direction parallel to the axis of rotation of the workpiece (the axial direction) to the direction normal to this axis (the circumferential direction), covering a range of angles between 0 and 90◦ . These directions are shown in Fig. 3.50. The sequences of gray-scale images acquired by the camera are stored in the computer. In the post-process stage, these images are converted into temperature-scale images (temperature distribution) using appropriate calibration curves.

202

Tribology of Metal Cutting

Fig. 3.50. Schematic representation of the directions of temperature measurements using the thermal imaging equipment (Courtesy of J.C. Outeiro).

Examples of measurements are shown in Figs. 3.51 and 3.52 for the cutting tool with the following cutting geometry: normal rake angle γn = −4.29◦ , the normal flank angle, αn = 4.29◦ , normal wedge angle, βn = 90◦ ; inclination angle of the cutting edge, λs = −14◦ , tool cutting edge angle, κr = 72◦ , nose radius, rn = 0.8 mm and tool cutting edge radius ρce = 0.044 mm. Although it has a number of obvious advantages, infrared thermography suffers some limitations: • The most severe and relevant to metal cutting studies is that it can only be applied to determine the temperature of surface if this surface is available for direct observation

(a)

(b)

Fig. 3.51. An example of temperature measurement: infrared images obtained with the camera placed in the (a) circumferential and (b) axial directions, showing the tool, chip and workpiece (Courtesy of J.C. Outeiro).

Tribology of the Tool–Chip and Tool–Workpiece Interfaces

(a)

203

(b)

Fig. 3.52. Temperature distribution on the chip and on the uncoated tool, obtained with the camera placed in the (a) circumferential and (b) axial directions. Cutting conditions: work material steel AISI 1045, uncoated tool, cutting speed ν = 125 m/min, feed f = 0.05 mm/rev and depth of cut dw = 5 mm.

by the infrared camera. As seen in Fig. 3.50, the temperature of the chip’s free surface and one side of the tool chip contact can only be measured. As such, the maximum contact temperature and its exact location with respect to the cutting edge may not be determined properly. As seen in Figs. 3.51 and 3.52, the maximum temperature is measured at the region closely adjacent to the cutting edge while it is well known that the maximum temperature under similar cutting conditions occurs at a certain distance from this edge [36,37,57]. • Another factor that can lead to erroneous temperature readings is the geometry of the surface being scanned. A concave surface tends to concentrate more energy into the scanned area, just as a magnifying shaving mirror focuses sunlight, and presents a higher emissivity. Similarly, a convex surface disperses the energy with an opposite effect, showing a lower emissivity. Flat surfaces, especially polished ones, do not emit radiation equally in all directions so the angle at which a flat surface is viewed will have an effect. The more the angle deviates from 90◦ to the surface, the lower the apparent emissivity becomes, and the greater is the possible temperature error if this is not taken into consideration. And for highly reflective objects, the polarization effect has to be taken into account. • An accurate knowledge of surface emissivity is essential for applications in infrared measurements. Direct measurements of surface emissivity are difficult. The true material emissivity value is a continuous changing property (dynamic) based upon many material and application factors during the heat cycle. As with temperature, emissivity depends significantly upon the wavelength. In order to make an

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• The application of this technique is limited to dry cutting conditions. • When classical infrared scanning cameras are used, it is difficult to evaluate with sufficient accuracy the high temperature gradients and high dynamic phenomena, which is the case in the metal cutting process. • High cost of infrared cameras. Over the recent years, low-cost camera solutions were being applied to the determination of the temperature distribution on the tool and chip in orthogonal cutting [115,126,127]. These CCD cameras operate in the near infrared spectrum (wavelength between 400 and 1100 nm) and, therefore, they are classified as Very Short Wave (VSW) cameras [128], compared to the infrared cameras referred above, which are classified as Short Waves (SW) and Long Waves (LW) cameras, respectively [128].

Thermocouples. Researchers in the field of metal cutting have been using thermocouples since the 1920s [34]. There are three basic types of thermocouples used in metal cutting: embedded, running and tool–work. The running and tool-work thermocouple techniques are specific to metal cutting studies [34,36,57] while embedded thermocouples utilized well-developed methodology used in temperature measurements in various applications [129–131]. The principle of temperature measurement with an embedded thermocouple is shown in Fig. 3.53. The thermocouple is placed in a small hole made in the cutting tool. The diameter of this hole should be as small as possible to reduce disturbances which may have an appreciable effect on the distribution of the thermal energy in the cutting tool and thus the measured temperatures. Experience shows [36] that temperatures can be measured with sufficient accuracy when the terminal thermocouple junction is pressed against the cutting insert (the bottom of the hole) with a force of no less than 50 N. As this is not always possible, it is recommended that the terminal end is welded to the insert using condenser welding when HSS inserts are used. By placing thermocouple holes in different positions of the insert, the temperature field and/or distribution can be determined. A useful method to obtain such a field using a single thermocouple is as follows: a thermocouple is initially placed in the most remote (from the cutting edge) point of insert and then by regrinding the flank and the rake surfaces in any desired sequence, the relative location of the thermocouple is moved to the desirable point relative the cutting edge. A standard thermocouple and standard calibration procedure can be used with the embedded thermocouple technique in accordance with the ASTM Manual on the Use of Thermocouples in Temperature Measurement (ASTM manual Pcn: 28-012093-40 by committee E20 on temperature measurements, 1993), with other international standards (for example, Thermocouples (IEC-60584), Industrial Platinum Resistance Thermometer Sensors (IEC 751), Temperature Measurement Thermocouples (ANSI-MC96.1)). The output of an embedded thermocouple is in the millivolt range and may be measured by

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Approx. 0.3–0.5 dia. Approx. 0.3–0.4 mm

Carbide insert

Cutting tool

Rigrindable flank

Potentiometer

Fig. 3.53. Embedded thermocouple.

a digital millivoltmeter. The voltmeter is basically a current-sensitive device; hence, the meter reading will be dependent on both the electromotive force (e.m.f.) generated by the thermocouple and the total circuit resistance, including the resistance of connecting wires. Therefore, the whole system, including the thermocouple, connecting wires and millivoltmeter should be calibrated directly to furnish a reasonably accurate temperature measurement. A large number of commercially available electronic voltmeters (for example by Omega Engineering Inc) and data acquisition systems (for example by National Instruments Co) are suitable for thermocouple measurements. Among them, those providing a digital output which can be used for computer processing of the temperature data are most suitable, particularly when the cutting temperature is measured simultaneously with the cutting force and/or other outputs of the cutting system. The technique of temperature measurements in metal cutting with embedded thermocouples suffers some limitations: • It cannot be used to measure temperatures at the tool–chip and tool workpiece interfaces directly as the thermocouple is located at a certain distance from the surface. As known from Ref. [37], a very great temperature gradient (along a normal to the tool contact area toward in-depth of the tool material) exists at the interfaces so the temperature reading provided by an embedded thermocouple may not reflect the maximum temperature and its exact location. This drawback becomes more severe when modern low thermal conductivity tool materials are used.

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• The exact contact condition at the bottom of the hole (Fig. 3.53) affecting temperature measurements is not known. • This technique cannot be used to measure the cutting temperature as the average integral temperature. Running thermocouples are used when one wants to measure temperatures in the deformation zone, i.e. at the partially formed chip and at the interfaces. The array of running thermocouples to measure temperature distribution in the deformation zone and partially formed chip is shown in Fig. 3.54(a). Insulated constantan wires of 0.12 mm diameter are embedded in holes of different depths in the layer to be removed by the tool. When this layer approaches the deformation zone, it deforms first elastically and then plastically so that the wires are gripped securely in the holes, forming thermocouples in this way. The cold junction of the thermocouples is secured to the workpiece far enough from the

340

Chip 220

460

170

Tool

68

490 580

125

625

20°C

Workpiece

(a) A1

(b)

B1

q (°C) Titanium alloy 1000

Ao

800

Bo

600

Steel AISI 1045

Steel AISI 1045

C1

D1Do

Co

400 ) 600 q (°C

Titanium alloy

(c)

0.2 0.4 0.6 0.8 1.0 1.2 1.4 (mm)

0.2 0.4 0.6 0.8 1.0 (mm)

(d)

Fig. 3.54. Temperature measurements with running thermocouples: (a) schematic representation for measuring temperatures in the deformation zone and partially formed chip, (b) an example of reconstructed temperature field in the deformation zone and the partially formed chip, (c) schematic representation for the assessment temperature distributions over the tool–chip and tool–workpiece interfaces and (d) an example of the results obtained.

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deformation zone to keep this cold junction at room temperature. Arranged in this way, thermocouples produce the e.m.f. while the layer being removed passes the deformation zone, becoming the chip that moves over the tool rake face. Using the results of such measurements, the temperature field can then be reconstructed, as shown in an example in Fig. 3.54(b) for AISI 1045 steel work material machined on a shaper with the uncut chip thickness t1 = 2 mm using the P10 carbide tool having a rake angle of γ = 10◦ . Figure 3.54(c) shows the use of the running thermocouple technique for measuring temperature distribution at the tool–chip and tool–workpiece interfaces. A tube-workpiece is used for experiments. A hole of 0.8–1.2 mm diameter is drilled in the workpiece, and a thin-wall protective tube is inserted into this hole. Then, two insulated wires made of thermocouple materials (for instance, one from chromel and the other from copel) are inserted into the tube, and their ends A1 B1 and C1 D1 are connected to two amplifiers on a data acquisition board. In cutting, the protective tube (made of material similar to that of the workpiece) is cut into two portions, as shown in Fig. 3.54(c). As such, two running thermocouples are formed having outputs A0 B0 and C0 D0 . The first thermocouple runs over the tool–chip interface, registering a temperature distribution along the tool–chip contact length while the second thermocouple runs over the tool–workpiece interface, registering a temperature distribution along the tool–workpiece contact length. Figure 3.54(d) shows an example of the obtained result for two work materials: steel AISI 1045 and Ti Grade 1 alloy. Other cutting parameters were as follows: cutting speed ν = 120 m/min, feed f = 0.26 mm/rev, depth of cut dw = 3 mm, tool material – M30 carbide, rake angle γn = 0◦ , flank angle αn = 12◦ . Although the technique of temperature measurements in metal cutting with running thermocouples is the only feasible method of obtaining temperature distributions at the interfaces and to determine the location of the points of maximum temperature at these interfaces with respect to the cutting edge, it has some limitations: • The use of this method requires extensive training of the experimentalist and proper design of a setup. The proper reading can be obtained only by an experienced specialist. To the best of the author’s knowledge, no one company, college or university provides such a training today. • Each test requires a great deal of preparation time. Tool–work thermocouple. This is the most widely used method for measuring temperature in metal cutting studies [34,36]. With this method, the average integral temperature at the tool–chip and tool–workpiece interfaces, defined earlier as the cutting temperature, is measured. Because the exact nature of formation of the signal measured by this thermocouple is not known, the result of measurements cannot be compared with the results of analytical studies or measurements obtained using other experimental techniques. Unfortunately, this issue is not well understood, so there are a number of attempts made to compare the results obtained using a tool–work thermocouple to those obtained in analytical and numerical studies [88,132].

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Workpiece

Mercury contact

Spindle Insulation

Amplifier

Cutting tool

PC computer with DAB

ω ε

2334 23334 α = 567890 δ

δ

φ 34456ψ

δ

Fig. 3.55. Tool–work thermocouple circuit.

Figure 3.55 shows the principle of this method. Because the tool and work materials are normally different, their contact at the tool–chip and tool–workpiece interfaces forms the hot junction of the tool–work thermocouple. The components of this thermocouple are insulated from the machine and fixtures to eliminate noise in the output signal. This output signal is the e.m.f. voltage which is amplified and then is fed to the data acquisition board plugged into a computer for further analysis. The major problem with tool–work thermocouples is their proper calibration [36]. The objective of the calibration is to obtain a calibration curve (normally a straight line [34,88,133]) that correlates the e.m.f. produced by the thermocouple and temperature. Although the literature offers a wide range of calibration procedures for this thermocouple, two basically different methods are common nowadays. The first one [34,57,68] involves comparing the e.m.f. produced by the tool–work thermocouple and a standard thermocouple placed in a thermoinsulated container with a molten metal (normally, tin or lead) having uniform temperature. As such, the tool–work thermocouple is made of a rod of the tool material and a long chip of the work material is held in tight contact at their ends. If the properties of work material do not allow forming a long chip, then a rod made of the work material is used. The second method is to calibrate a tool–work thermocouple when the tool is brought in tight contact with the workpiece and the heat

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is applied by an oxygen–acetylene or propane torch [88]. As such, a standard reference thermocouple is spot welded into the cutting insert at the would be tool–chip interface. Since the calibration is critical to obtaining accurate results, a few severe problems associated with the known calibrations have to be pointed out: • Circuits used in calibration and in actual cutting are not the same. Commonly, the samples that represent the tool and chip are not even in contact (Fig. 12.2 in Ref. [34], Fig. 7.3(a) in Ref. [57]). Even if they are brought in close contact, the actual contact area is not the same as in reality and the contact pressure is well below than that in actual cutting. Besides, the contact between the tool flank and the workpiece taking place in actual cutting is completely ignored and a mercury contact connecting the rotating spindle with the amplifier is not present in the calibration circuit. • Lead or tin bath is used in calibrations to obtain the uniform maximum calibration temperature. However, the temperature of molten lead is far below those expected in cutting. Since the calibration curve for a natural thermocouple may not be linear (Fig. 12.3 in Ref. [34]), it is next to impossible to extrapolate the obtained results, i.e. the obtained calibration curves may contain significant errors. The same problem exists with torch heating. • Since the specimen representing the tool in calibrations has rather restricted length, it is very difficult to keep the cold junction of a natural thermocouple at constant temperature. As pointed out in Ref. [57], it is particularly true when small indexable tool inserts are used. The same problem occurs with obtaining a sufficiently long chip for the workpiece materials of relatively low ductility. One of the possible methods for calibrating the natural thermocouples is based on the above-discussed first principle of thermoelectric circuit can be used [36,90]. According to this principle, a third metal, connected in the circuit, does not change the net e.m.f. of the circuit if the new connection is at the same temperature as the initial junction [36]. An arrangement for calibration is shown in Fig 3.56(a). The workpiece 1 is cut by two geometrically similar cutters 2 and 3 made of different tool materials having similar thermal conductivity. Because both tools work in the same cutting regime, it may be assumed that both tools have the same contact temperature so that the requirement of the second law is justified when the workpiece is considered as the third metal in the circuit. The arrangement also includes a two-position switch 4 and an analog–digital millivoltmeter 5 with built-in amplifier. The output of the millivoltmeter 5 is connected to a computer 6. The calibration procedure includes two successive stages. In the first stage, a relatively low-melting-point material (for instance, aluminum) is used as the work material and its melting point is stored in the computer program used in the calibration. The switch 4 is in the a-position. When cutting starts, the cutting speed is gradually increased up to the point when the work material begins to melt at the tool–chip interface of both cutters. The e.m.f. E1 corresponding to this point is registered by the millivoltmeter 5 and then is stored in the computer program. Several tests with different work materials can be carried out to obtain calibration curve Emf = f(θ), as shown in Fig. 3.56(b).

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E

E3

3

E = j (q)

2 1 4

b

E = f (q)

E2 a

6

5

E1

0

(a)

q1

q2

q

(b)

Fig. 3.56. Arrangement for calibration of tool–work thermocouple.

At the second stage of calibration, the actual work material is used. In a given cutting regime, the e.m.f. of the two-cutter thermocouple is measured to be E2 using which the computer calculated the corresponding temperature θ2 . After this measurement is taken, the computer gives a signal to a servomechanism for fast withdrawal of the second cutter 3 in the direction shown by an arrow in Fig. 3.56(a) and simultaneously the switch 4 is moved to the b-position. The cutter 1 is still working at the same cutting regime. A new e.m.f. E3 is measured. Although the cutting temperature θ2 does not change, E2 = E3 as the latter was measured using a new tool–work thermocouple. Using a few measuring points (cutting regimes) and corresponding differences in the e.m.f.s, the computer calculates the corrected calibration curve Emf = ϕ(θ) which is used in further experiments.

3.4.3 Generalizations Because the temperature generated in machining is one of the major factors that determine tool life and that limit the cutting rate, its proper assessment, correlation with the characteristics and parameters of the cutting system and control are of enormous significance in metal cutting theory and practice as well as in the tool and machine design and selection. The results of the theoretical and experimental studies on temperatures in metal cutting can be summarized as follows: • There are two most relevant temperatures found in metal cutting: First is the average integral contact temperature as measured by the tool–work thermocouple technique.

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As shown in the practice of metal cutting research [68,85,88,89], this is the most stable and relevant characteristic that can be measured with high accuracy, great repeatability and reproducibility. Second is the maximum contact temperature and the point of its location with respect to the cutting edge. This temperature may cause the plastic lowering of the cutting edge and catastrophic tool failure limiting the allowable cutting speed. • Analytical and numerical methods used for the assessment of temperatures in metal cutting suffer severe drawbacks, so their results can hardly be used in any practical application. The only proper way to change this state of the art is to use the proper metal cutting model with realistic contact conditions at the tool–chip and tool– workpiece interfaces. As for numerical methods, the proper procedure should be fully developed to account for large plastic deformation and fracture taking place in metal cutting. • The similarity method is much less sensitive to the particular model used in modeling particularly when applied to the thermal analysis of metal cutting [36,68]. This method is much more realistic than the analytical and numerical methods developed so far. Relatively simple, straightforward and physically justifiable calculations of temperature in metal cutting used in this method should prevent further attention of researchers and practitioners. In the author’s opinion, this method should be put as the basis of software packages for the simulation of metal cutting. • Among the known methods used today for experimental determination of temperatures in metal cutting, the tool–work thermocouple technique is the most accurate [89,134] although the infrared thermography technique also has some potential. In the author’s opinion, the tool–work thermocouple technique should be used on all modern metal cutting machines as part of their control system. Although one may argue that additional cost might be needed for electrical insulation of fixturing and tooling, the resulting gain will definitely overlap these costs. First and foremost, the optimal control of the cutting process can be achieved if such a technique is available on the machine tool (see Chapter 4). Second, it is conclusively proven that electrical insulation of fixturing and tooling causes the tool life to increase by 10–20% because it prevents electro-diffusion tool wear predominant at high cutting speeds [135,136].

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[6] Finnie, I., Shaw, M.C., The friction process in metal cutting, Transactions of ASME, 77 (1956), 1649–1657. [7] Usui, E., Takeyma, H., A photoelastic analysis of machining stresses, ASME Journal of Engineering for Industry, 81 (1960), 303–308. [8] Strenkowski, J.S., Moon, K.-J., Finite element prediction of chip geometry and tool/workpiece temperature distributions in orthogonal metal cutting, ASME Journal of Engineering for Industry, 112 (1990), 313–318. [9] Komvopoulos, K., Erpenbeck, S.A., Finite element modeling of orthogonal metal cutting, ASME Journal of Engineering for Industry, 113 (1991), 253–267. [10] Lin, Z.C., Pan, W.C., Lo, S.P., A study of orthogonal cutting with tool flank wear and sticking behaviour on the chip–tool interface, Journal of Materials Processing Technology, 52 (1995), 524–538. [11] Lin, Z.C., Lin, S.Y., A coupled finite element model of thermo-elastic-plastic large deformation for orthogonal cutting, Journal of Engineering Materials and Technology, 114 (1992), 218–226. [12] Strenkowski, J.S., Carroll, J.T., A finite element model of orthogonal metal cutting, ASME Journal of Engineering for Industry, 107 (1985), 349–354. [13] Endres, W.J., Devor, R.E., Kapoor, S.G., A dual-mechanism approach to the prediction of machining forces, Part 2: calibration and validation, ASME Journal of Engineering for Industry, 117 (1995), 534–541. [14] Olovsson, L., Nilsson, L., Simonsson, K., An ALE formulation for the solution of two-dimensional metal cutting problems, Computers and Structures, 72 (1998), 497–507. [15] Hahn, R.S., On the temperature development at the shear plane in the metal cutting process. In Proceedings of the First US Nat. Appl. Mech., ASME, New York, 1952, pp. 112–118. [16] Chao, B.T., Trigger, K.J., Cutting temperatures and metal cutting phenomena, ASME Journal of Engineering for Industry, 73 (1951), 777–793. [17] Lowell, M.R., Deng, Z., Experimental investigation of sliding friction between hard and deformable surfaces with application to manufacturing processes, Wear, 236 (1999), 117–127. [18] Challen, J.M., Oxley, P.L.B., An explanation of the different regimes of friction and wear using asperity deformation models, Wear, 53 (1979), 229–243. [19] Kayaba, T., Kato, K., Hokkirigawa, K., Theoretical analysis of the plastic yielding of a hard asperity sliding on a soft flat surface, Wear, 87 (1983), 151–161. [20] Kayaba, T., Hokkirigawa, K., Kato, K., Experimental analysis of the plastic yielding of a hard asperity sliding on a soft flat surface, Wear, 96 (1984), 255–265. [21] Challen, J.M., Oxley, P.L.B., A slip-line field analysis of the transition from local asperity contact to full contact in metallic sliding friction, Wear, 100 (1984), 171–193. [22] Komvopoulos, K., Saka, N., Suh, N.P., Plowing friction in dry and lubricated metal sliding, ASME Journal of Tribology, 108 (1986), 301–313.

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[23] Komvopoulos, K., Saka, N., Suh, N.P., The role of hard layers in lubricated and dry sliding, ASME Journal of Tribology, 109 (1987), 223–231. [24] Black, A.J., Kopalinsky, E.M., Oxley, P.L.B., An investigation of the different regimes of deformation which can occur when a hard wedge slides over a soft surface: the influence of the wedge angle, lubrication and prior plastic working of the surface, Wear, 123 (1988), 97–114. [25] Black, A.J., Kopalinsky, E.M., Oxley, P.L.B., Sliding metallic friction with boundary lubrication: an investigation of a simplified friction theory and of the nature of boundary lubrication, Wear, 137 (1990), 161–174. [26] Kopalinsky, E.M., Investigation of surface deformation when a hard wedge slides over a soft surface, ASME Journal of Tribology, 114 (1992), 100–106. [27] Black, A.J., Kopalinsky, E.M., Oxley, P.L.B., Asperity deformation models for explaining the mechanisms involved in metallic sliding friction and wear – a review, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 207 (1993), 335–353. [28] Sutcliffe, M.P.F., Surface asperity deformation in metal forming processes, International Journal of Mechanical Sciences, 30 (1988), 847–868. [29] Yang, Y., Torrance, A.A., Oxley, P.L.B., Modelling mechanical wear processes in metallic sliding friction. Journal of Physics D: Applied Physics, 29 (1996), 600–608. [30] Torrance, A.A., Buckey, T.R., A slip-line field model of abrasive wear, Wear, 196 (1996), 35–45. [31] Kopalinsky, E.M., Oxley, P.L.B., An investigation of the mechanics of sliding metallic wear under lubricated conditions, Wear, 214 (1998), 38–46. [32] Byers, J.P., Laboratory evaluation of metalworking fluids, in Metalworking Fluids, J.P. Byers, Editor. Marcel Dekker, New York, 1994, pp. 191–221. [33] Komanduri, R., Larsen-Basse, J., Tribology: the cutting edge, Mechanical Engineering, 111 (1989), 74–79. [34] Shaw, M.C., Metal Cutting Principles, Oxford Science Publications, Oxford, 1984. [35] Oxley, P.L.B., Mechanics of Machining: An Analytical Approach to Assessing Machinability, John Wiley & Sons, New York, US, 1989. [36] Astakhov, V.P., Metal Cutting Mechanics, CRC Press, Boca Raton, US, 1998. [37] Trent, E.M., Wright, P.K., Metal Cutting, Butterworth-Heinemann, Boston, US, 2000. [38] Arsecularatne, J.A., On tool–chip interface stress distributions, ploughing force and size effect in machining, International Journal of Machine Tools and Manufacture, 37 (1997), 885–899. [39] Doyle, E.D., Horne, J.G., Tabor, D., Frictional interactions between chip and rake face in continuous chip formation, Proceedings of Royal Society, London A, 366 (1979), 173–183. [40] Coker, E.G., Filon, L.N.G., Treatise on Photoelasticity, Cambridge University Press, Cambridge, 1931. [41] Zeichev, A.G., Optical Methods of Stress Analysis, Frontier Publishing, Moscow, 1934.

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[42] Frocht, M.M., Thomson, R.A., Studies in Photoelasticity. In Proceedings of the Third U.S National Congress of Applied Mechanics, 1958, pp. 25–34. [43] Ocushiri, M., Fukuii, S., Studies of cutting action by means of photoelasticity, Journal of the Society of Precision Mechanics of Japan, 1 (1934), 508–514. [44] Andreev, G.S., Photoelastic study of stresses in a cutting tool using cinematography (in Russian), Vestnyk Machinostroeniya, 38 (1958), 54–57. [45] Kattwinkel, W., Untersuchungen an schneiden spanender werkzeuge mit hilfe der spannungsoptic, Industry-Anzeiger, 37 (1957), 29–33. [46] Takeyama, H., Usui, H., The effect of tool–chip contact area in metal cutting, ASME Journal of Engineering for Industry, 79 (1958), 1089–1096. [47] Chandrasekaran, H., Kapoor, D.V., Photoelastic analysis of tool–chip interface stresses, ASME Journal of Engineering for Industry, 87 (1965), 495–502. [48] Amini, E., Photoelastic analysis of stresses and forces in steady cutting, Journal of Strain Analysis, 3 (1968), 206–213. [49] Okushima, K., Kakino, Y., Hagihara, S., Hasimito, H., A stress analysis in the orthogonal cutting by photo elasto-plasticity method, Bulletin of Japanese Society of Precision Engineering, 5 (1971), 1–7. [50] Barrow, G., Graham, W., Kurimoto, T., Leong, Y.F., Determination of rake face stress distribution in orthogonal machining, International Journal of Machine Tool Design and Research, 22 (1982), 75–85. [51] Bagachi, A., Wright, P.K., Stress analysis in machining with the use of sapphire tools, Proceedings of Royal Society of London A, 409 (1987), 99–113. [52] Loladze, T.N., Strength and Wear of Cutting Tools (in Russian), Mashgiz, Moscow, 1958. [53] Gordon, M.B., The applicability of binomial law to the process of friction in the cutting of metals, Wear, 10 (1967), 274–290. [54] Kato, S., Yamaguchi, K., Yamada, M., Stress distribution at the interface between the tool and chip in machining, ASME Journal of Engineering for Industry, 93 (1972), 683–689. [55] Boothroyd, G., Knight, W.A., Fundamentals of Machining and Machine Tools, Second Edition. Marcel Dekker, New York, 1989. [56] Gorczyca, F.Y., Application of Metal Cutting Theory, Industrial Press, New York, 1987. [57] Stenphenson, D.A., Agapiou, J.S., Metal Cutting Theory and Practice, Marcel Dekker, New York, 1996. [58] Childs, T.H.C., Maekawa, K., Obikawa, T., Yamane, Y., Metal Machining. Theory and Application, Arnold, London, 2000. [59] Schey, J.A., Metal Deformation Processes: Friction and Lubrication, Marcel Dekker, New York, 1970. [60] Schey, J.A., Tribology in Metalworking, American Society for Metals, Metals Park, Ohio, 1983.

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[61] Usui, E., Shirakashi, T., Mechanics of metal cutting – from “description” to “predictive” theory, in On the Art of Cutting Metals – 75 Years Later, Phoenix, Arizona, ASME, New York, 1982, pp. 13–36. [62] Buryta, D., Sowerby, R., Yellowley, Y., Stress distributions on the rake face during orthogonal machining, International Journal of Machine Tools and Manufacture, (1994), 721–739. [63] Machado, A.R., Wallbank, J., The effect of extremely low lubricant volumes in machining, Wear, 210 (1997), 76–82. [64] Roth, R.N., Oxley, P.L.B., A slipline field analysis for orthogonal machining based on experimental flow fields, Journal of Mechanical Engineering Science, 14 (1972), 86–97. [65] DeGarmo, E.P., Black, J.T., Kohser, R.A., Materials and Processes in Manufacturing, Prentice Hall, Upper Saddle River, NJ, 1997. [66] Hsu, T.C., A study of normal and shear stresses on a cutting tool, ASME Journal of Engineering for Industry, 94 (1966), 51–64. [67] Lin, Z.-C., Lo, S.-P., A study of deformation of the machined workpiece and tool under different low cutting velocities with an elastic cutting tool, International Journal of Mechanical Science, 40 (1998), 663–668. [68] Silin, S.S., Similarity Methods in Metal Cutting (in Russian), Moscow, Machinostroenie, 1979. [69] Poletica, M.F., Contact Loads on Tool Interfaces (in Russian), Machinostroenie, Moscow, 1969. [70] Abuladze, N.G., The tool–chip interface: determination of the contact length and properties (in Russian), in Machinability of Heat Resistant and Titanium Alloys, Kyibashev Regional Publ. House, Kyibashev, Russia, 1962, pp. 87–96. [71] Hills, D.A., Nowell, D., Sackfield, A., Mechanics of Elastic Contact, ButterworthHeinmann, London, 1993. [72] Muskhelishvili, N.I., Some Basic Problems of the Mathematical Theory of Elasticity, Sijthoff & Noordhoff Int. Pub., Leyden, 1977. [73] Astakhov, V.P., Outeiro, J.C., Modeling of the contact stress distribution at the tool–chip interface, Machining Science and Technology, 9 (2005), 85–99. [74] Galin, L.A., Contact Problems in the Theory of Elasticity (in Russian), Gostechnozdat, Moscow, 1953. [75] Astakhov, V.P., Shvets, S.V., A system concept in metal cutting, Journal of Materials Processing Technology, 79 (1998), 189–199. [76] Poletica, M.F., Contact Loads on Cutting Tool Interface Surfaces (in Russian), Machinostroenie, Moscow, 1969. [77] Astakhov, V.P., Shvets, S., The assessment of plastic deformation in metal cutting, Journal of Materials Processing Technology, 146 (2004), 193–202. [78] Klushin, M.I., Metal Cutting: Basics of Plastic Deformation of the Layer been Removed, Mashgiz, Moscow, Russia, 1958.

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[79] Liu, G., Wang, Q., Thermoelastic asperity contacts, frictional shear, and parameter correlations, Journal of Tribology, 122 (2000), 300–307. [80] Spaans, C., Treatise on the streamlines and the stress, strain, and strain rate distribution, and on stability in the primary shear zone in metal cutting, ASME Journal of Engineering for Industry, 94 (1972), 690–696. [81] Isakov, E., Mechanical Properties of Work Materials, Hanser Gardener Publications, Cincinnati, OH, 2000. [82] Shuster, L.S.H., Adhesion Processes at the Tool–Work Material Interface (in Russian) Machinostroenie, Moscow, 1988. [83] Chen, N.N.S., Pun, W.K., Stresses at the cutting tool wear land, International Journal of Machine Tools and Manufacture, 28 (1988), 79–92. [84] Altintas, Y., Manufacturing Automation. Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design, Cambridge University Press, Cambridge, 2000. [85] Makarow, A.D., Optimization of Cutting Processes (in Russian), Machinostroenie, Moscow, 1976. [86] Komarovsky, A.A., Astakhov, V.P., Physics of Strength and Fracture Control: Fundamentals of the Adaptation of Engineering Materials and Structures, CRC Press, Boca Raton, 2002. [87] Astakhov, V.P., Tribology of metal cutting, in Mechanical Tribology, H. Liang, G.E. Totten, Editors. Marcel Dekker, New York, 2004, pp. 307–346. [88] Leshock, C.E., Shin, Y.C., Investigation on cutting temperature in turning by a tool-work thermocouple technique, Journal of Manufacturing Science and Engineering, 119 (1997), 502–508. [89] Silva, M.B., Wallbank, J., Cutting temperature: prediction and measurement methods – a review, Journal of Materials Processing Technology, 88 (1999), 195–202. [90] Reznikov, A.N., Reznikov, L.A., Thermal Processes in Machining Systems (in Russian), Machiostroenie, Moscow, 1990. [91] Komanduri, R., Hou, Z.B., Thermal modeling of the metal cutting process. Part I – Temperature rise distributing due to shear plane heat source, International Journal of Mechanical Science, 42 (2000), 1715–1752. [92] Komanduri, R., Hou, Z.B., Thermal modeling of the metal cutting process – Part II: temperature rise distribution due to frictional heat source at the tool–chip interface, International Journal of Mechanical Science, 43 (2001), 57–88. [93] Komanduri, R., Hou, Z.B., Thermal modeling of the metal cutting process – Part III: temperature rise distribution due to the combined effect of the shear plane heat source and the tool–chip interface frictional source, International Journal of Mechanical Science, 43 (2001), 89–107. [94] Ramesh, M.V., Seetharaman, K.N., Ganesan, N., Kuppuswamy, G., Finite element modelling of heat transfer analysis in machining of isotropic materials, International Journal of Heat and Mass Transfer, 43 (1999), 1569–1583. [95] Ng, E.-G., Aspinwall, D.K., Brazil, D., Monaghan, J., Modelling of temperature and forces when orthogonally machining hardened steel, International Journal of Machine Tools and Manufacture, 39 (1999), 885–903.

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[96] Lazoglu, I., Altintas, Y., Prediction of tool and chip temperature in continuous and interrupted cutting, International Journal of Machine Tools and Manufacture, 42 (2002), 1011–1022. [97] AdvantEdge™ Modelingsoftware. ThirdWavesystems, http://www.thirdwavesys.com, 2004. [98] Chan, C.L., Chandra, A., A boundary element method analysis of the thermal aspects of metal cutting processes, ASME Journal of Engineering for Industry, 113 (1991), 311–319. [99] Atkins, A.G., Mai, Y.W., Elastic and Plastic Fracture: Metals, Polymers. Ceramics, Composites, Biological Materials, John Wiley & Sons, New York, 1985. [100] Atkins, A.G., Modelling metal cutting using modern ductile fracture mechanics: quantitative explanations for some longstanding problems, International Journal of Mechanical Sciences, 43 (2003), 373–396. [101] Atkins, A.G., Modelling metal cutting using modern ductile fracture mechanics: qualitative explanations for some longstanding problems, International Journal of Mechanical Sciences, 45 (2003), 373–396. [102] Abramowitz, M., Stegun, I.A., ed. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. Dover, New York, 1972. [103] Spanier, J., Oldham, K.B., The error function erf(x) and its complement erfc(x), in An Atlas of Functions, Hemisphere, Washington, DC, 1987, pp. 385–393. [104] Smart, E.F., Trent, E.M., Temperature distribution in tools used for cutting iron, titanium and nickel, International Journal of Production Research, 13 (1975), 265–290. [105] Wright, P.K., Trent, E.M., Metallurgical methods of determining temperature gradients in cutting tools, Journal of the Iron and Steel Institute, 211 (1973), 364–368. [106] Mills, B., Wakeman, D.W., Aboukhashaha, A., A new technique for determining the temperature distribution in high speed steel cutting tools using scanning electron microscopy, Annals of the CIRP, 29 (1980), 73–77. [107] LoCastro, S., LoValvo, E., Piacentini, M., Ruisi, V.F., Lucchini, E., Maschio, S., Lonardo, P., Cutting temperatures evolution in ceramics tools: experimental tests, numerical analysis and SEM observations, Annals of the CIRP, 43 (1994), 73–76. [108] Kato, S., Yamaguchi, Y., Watanabe, Y., Hiraiwa, Y., Measurement of temperature distribution within tool using powders of constant melting point, ASME Journal of Engineering for Industry, 98 (1976), 607–613. [109] Dearnley, P.A., New technique for determining temperature distribution in cemented carbide cutting tool, Metals Technology, 10 (1983), 205–210. [110] Nordgren, A., Chandrasekaran, H., Measurement of cutting tool temperature using binder phase transformation in cemented carbide tools, Swedish Institute for Metals Research, 1995. [111] Outeiro, J.C., Dias, A.M., Lebrun, J.L., Experimental assessment of temperature distribution in three-dimensional cutting process, Machining Science and Technology, 8 (2004), 357–376. [112] Boothroyd, G., Temperatures in orthogonal metal cutting, Proceedings of the Institution of Mechanical Engineers, 177 (1963), 789–802.

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[113] Malitzki, H., Radtke, U., Barnikow, A.-M., Messung von temperaturfeldern im spanwurzelgebiet beim drehen, Feingeratetechnik, 28 (1979), 68–71. [114] Spur, G., Beyer, H., Erfassung der temperaturverteilung am drehmeissel mit hilfe der fernsehthermographie, Annals of the CIRP, 22 (1973), 3–4. [115] Le Calvez, C., Etude des Aspects Thermiques et Métallurgiques de la Coupe Orthogonale d’un Acier au Carbone. Thèse de Doctorat, Ecole Nationale Superieure d’Arts et Mètiers, Paris, 1995. [116] Barrow, G., A review of experimental and theoretical techniques for assessing cutting temperatures, Annals of the CIRP, 19 (1973), 551–557. [117] Kottenstette, J.P., Measuring tool–chip interface temperatures, ASME Journal of Engineering for Industry, 108 (1986), 101–104. [118] Ueda, T., Sato, M., Nakayama, R., The temperature of a single crystal diamond tool in turning, Annals of the CIRP, 47 (1998), 41–44. [119] Ueda, T., Hosokawa, A., Yamamoto, A., Studies on temperature of abrasive grains in grinding – application of infrared radiation pyrometer, ASME Journal of Engineering for Industry, 107 (1985), 127–133. [120] Herchang, A., Yang, W.J., Heat transfer and tool life of metal cutting tools in turning, International Journal of Heat and Mass Transfer, 41 (1998), 613–623. [121] Vernaza-Pena, K.M., Mason, J.J., Li, M., Experimental study of the temperature field generated orthogonal machining of an aluminum alloy, Experimental Mechanics, 42 (2002), 221–229. [122] Zehnder, A.T., Plasticity induced heating in the fracture and cutting of metals, in Thermo Mechanical Fatigue and Fracture, M.H. Aliabadi, Editor. WIT Press, Southampton, 2002, pp. 209–244. [123] Kwon, P., Schiemann, T., Kountanya, R., An inverse estimation scheme to measure steadystate tool–chip interface temperature using an infrared camera, International Journal of Machine Tools and Manufacture, 41 (2001), 1015–1030. [124] Young, H.T., Chou, T.L., Investigation of edge effect from the chip-back temperature using IR thermographic techniques, Journal of Material Processing Technology, 52 (1995), 213–224. [125] Chu, T.H., Wallbank, J., Determination of the temperature of a machined surface, ASME Journal of Manufacturing Science and Engineering, 120 (1998), 259–263. [126] Outeiro, J.C., Comportamento do Aço AISI 316L em Torneamento Ortogonal, Departamento Engenharia Mecânica, Universidade de Coimbra, Coimbra, 1996. [127] M’Saoubi, R. Le Calvez, C., Changeux, B., Lebrun, J.L., Thermal and microstructural analysis of orthogonal cutting of low alloyed carbon steel using an infrared-charge-coupled device camera technique, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 216 (2002), 153–165. [128] Pajani, D., La Mesure Thermographique des Hautes Temperatures. Le Choix de la Bande Spectrale en Fonction des . . . l’Etendue d’Echelle, la Sensibilite et l’Exactitude, in http://perso.wanadoo.fr/dpajani/ineth/i_mesureht.html, Paris, França, 1996.

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[129] Pollock, D.D., Thermocouples: Theory and Properties, CRC Press, Boca Raton, 1991. [130] Kinzie, P.A., Thermocouple Temperature Measurement, John Wiley & Sons, New York, 1973. [131] Kirlin, T.W., Practical Thermocouple Thermometry, Instrument Society of America, Research Triangle Park, NC, 1999. [132] Ivester, R.W., Comparison of machining simulations for 1045 steel to experimental measurements, SME Paper TPO4PUB336, 2004, pp. 1–15. [133] Stephenson, D.A., Tool-work thermocouple temperature measurements – theory and implementation issues, ASME Journal of Engineering for Industry, 115 (1993), 432–437. [134] Wan, Y., Tang, Z.T., Liu, Z.Q., Ai, X., The assessment of cutting temperature measurements in high-speed machining, Materials Science Forums, 471–472 (2004), 162–166. [135] Bobrovsky, V.A., Electrodifussion Wear of Cutting Tools (in Russian), Machinostroenie, Moscow, 1970. [136] Bobrovsky, V.A., Drachev, O.I., Rubjakov, A.V., Cutting Non-Ferrous Materials (in Russian), Polytechnica, St. Petersburg, 2001.

CHAPTER 4

Cutting Tool Wear, Tool Life and Cutting Tool Physical Resource

4.1 Introduction In deforming processes used in manufacturing, concern over the wear is often overshadowed by considerations of forces or material flow. Except for hot extrusion, die life is measured in hours and days, or in thousands of parts [1]. In metal cutting, however, tool wear is a dominant concern because process conditions are chosen to give maximum productivity or economy, often resulting in tool life in minutes. Central to the problem are: high contact temperatures at the tool–chip and tool–workpiece interfaces that lead to the softening of tool material and promote diffusion and chemical (oxidation) wear; high contact pressures at these interfaces and sliding of freshly formed (juvenile) surfaces of the work material layers promote abrasive and adhesion wear [2]; cyclic nature of the chip formation process which can cause cracking due to thermal fatigue. Another tool wear mechanism is fretting wear. Fretting is a small amplitude oscillatory motion, usually tangential, between two solid surfaces in contact. Fretting wear occurs when repeated loading and unloading cause cyclic stresses, which induce surface or subsurface breakup and loss of material. Vibration is a common cause of fretting wear. The mentioned wear mechanisms (well discussed in [1]) may take place alone or, more frequently, in combination. The nature of tool wear, unfortunately, is not yet clear enough in spite of numerous investigations carried out over the last 50 years. Although various theories have been introduced hitherto to explain the wear mechanism, the complicity of the processes in the cutting zone hampers formulation of a sound theory of cutting tool wear. Cutting tool wear is a result of complicated physical, chemical, and thermomechanical phenomena. Because different “simple” mechanisms of wear (adhesion, abrasion, diffusion, oxidation, etc.) act simultaneously with predominant influence of one or more of them in different situations, identification of the dominant mechanism is far from simple, and most interpretations are subject to controversy [1]. These interpretations are highly subjective and based on the evaluation of the cutting conditions, possible temperature and contact stress levels, relative velocities and many other process paramagnets and factors. 220

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221

As a result, experimental, or post process methods, are still dominant in the known studies of tool wear [1–12] and only topological or simply, geometrical parameters of tool wear are selected and thus reported in tool wear and tool life studies. Although it might seem simple to measure and assess the topology and geometry of tool wear using modern equipment including image processing technique, in reality it is not so. Complicated and irregular shapes of tool wear patterns combined with complicated tool geometry and many possible ways and methods of tool wear measurement give rise to various methods of tool wear assessment. 4.2 Known Approaches 4.2.1 Types of tool wear In accordance with ANSI/ASME Tool Life Testing with Single-Point Turning Tools (B94.55M-1985), the principal types of tool wear, classified according to the regions of the tool they affect, are: • Rake face or crater wear (Fig. 4.1) produces a wear crater on the tool rake face. The depth of the crater KT is selected as the tool life criterion for carbide tools. The other two parameters, namely, the crater width KB and the crater center distance KM are important if the tool undergoes resharpening. • Relief face or flank wear (Fig. 4.1) results in the formation of a flank wear land. For the purpose of wear measurement, the major cutting edge is considered to be

KT

SECTION A-A KB

Zone

Plane Ps

KM

VBC Flank wear land

C A Crater

b

A

VBB max.

B VBB N VBN

Fig. 4.1. Types of wear on turning tools according to ANSI/ASME Tool Life Testing with SinglePoint Turning Tools (B94.55M-1985).

222

Tribology of Metal Cutting divided into the following three zones: (a) Zone C is the curved part of the cutting edge at the tool corner; (b) Zone N is the quarter of the worn cutting edge of length b farthest from the tool corner; and (c) Zone B is the remaining straight part of the cutting edge between Zones C and N. The maximum VBB max and the average VBB width of the flank wear are measured in Zone B, the notch wear VBN is measured in Zone N, and the tool corner wear VBC is measured in Zone C. As such, the following criteria for carbide tools are normally recommended: (a) the average width of the flank wear land VBB = 0.3 mm, if the flank wear land is considered to be regularly worn in Zone B; (b) the maximum width of the flank wear land VBB max = 0.6 mm, if the flank wear land is not considered to be regularly worn in Zone B. Besides, surface roughness for finish turning and the length of the wear notch VBN = 1 mm can be used. However, these geometrical characteristics of tool wear are subjective and insufficient. First, they do not account for the tool geometry (the flank angle, the rake angle, the cutting edge angle, etc), so they are not suitable to compare wear parameters of cutting tools having different geometries. Second, they do not account for the cutting regime and thus do not reflect the real amount of the work material removed by the tool during the tool operating time, which is defined as the time needed to achieve the chosen tool life criterion.

4.2.2 Wear curves and tool life Tool wear curves illustrate the relationship between the amount of flank (rake) wear and the cutting time (τm ) or the overall length of the cutting path (L). These curves are represented in linear coordinate systems using the results of cutting tests, where flank wear VBB max is measured after certain time periods (Fig. 4.2(a)) or after certain length of the cutting path (Fig. 4.2(b)). Normally, there are three distinctive regions that can be observed on such curves. The first region (I in Fig. 4.2(b)) is the region of primary or initial wear. Relatively high wear rate (an increase of tool wear per unit time or length

VBB max (mm)

mw (mg)

VBB max (mm)

mw (mg)

3

3

0.8

1.00 VB

0.75

VB 4

0.50

1

10

0.6

0.75

0.4

0.50

20

30

40

(a)

50

0.2

0.25

60 tm(min)

0

2 4

0.6 0.4

1

mw

0.25

0

0.8

1.00

2

mw

0.2

500

I

1000 1500 2000 2500 3000 L(m)

II

III

(b) Fig. 4.2. Typical tool rate curves for flank wear: (a) as a function of time and (b) as a function of cutting path (after Astakhov [25]).

Cutting Tool Wear, Tool Life and Cutting Tool Physical Resource

223

of the cutting path) in this region is explained by accelerated wear of the tool layers damaged during its manufacturing or resharpening. The second region (II in Fig. 4.2(b)) is the region of steady-state wear. This is the normal operating region for the cutting tool. The third region (III in Fig. 4.2(b)) is known as the tertiary or accelerated wear region. Accelerated tool wear in this region is usually accompanied by high cutting forces, temperatures and severe tool vibrations. Normally, the tool should not be used within this region. Tool wear depends not only on the cutting time or the length of the cutting path but also on the parameters of tool geometry (rake, flank, inclination angles, radius of the cutting edge, etc.), cutting regimes (cutting speed, feed, depth of cut), properties of the work material (hardness, toughness, structure, etc.), presence and properties of the cutting fluid and many other parameters of the machining system. In practice, however, the cutting speed is of prime concern in the consideration of tool wear. As such, tool wear curves are constructed for different cutting speeds keeping other machining parameters invariable. In Fig. 4.3, three characteristic tool wear curves (mean values) are shown for three different cutting speeds, ν1 , ν2 and ν3 . Because ν3 is greater than the other two, it corresponds to the fastest wear rate. When the amount of wear reaches the permissible tool wear VBBc , the tool is said to be worn out. Typically VBBc is selected from the range (0.15–1.00 mm) depending upon the type of machining operation, condition of the machine tool and quality requirements for the operation. It is often selected on the ground of process efficiency and often called the criterion of tool life. In Fig. 4.3, T1 is tool life when the cutting speed ν1 is used, T2 – when ν2 , and T3 – when ν3 is the case. When the integrity of the machined surface permits, the curve of maximum wear instead of the line of equal wear should be used (Fig. 4.3). As such, the spread in tool life between lower and higher cutting speeds becomes less significant. As a result, a higher productivity rate can be achieved which is particularly important when high-speed CNC machines are used. Tool life affects the choice of tool, selection of the process variables, economy of operation, and possibility of the process’s adaptive control. Standard tool-life testing

VBB

n3 Curve of maximum wear

n1
5

n1

4

VBBC

3

2

1 Line of equal wear

0 0

T3

T2

T1

tm

Fig. 4.3. Flank wear vs. cutting time at various cutting speeds (after Astakhov [25]).

224

Tribology of Metal Cutting

and representation includes Taylor’s tool life formula [13] νT n = CT ,

(4.1)

where T is tool life in minutes, CT is a constant into which all cutting conditions affecting tool life must be absorbed. Although Taylor’s tool life formula is still in wide use today and is in the very core of many studies on metal cutting including the level of national and international standards, one should remember that it was introduced in the year 1907 as a generalization of many years of experimental studies conducted in the nineteenth century using work and tool materials and experimental techniques available at that time. Since then, each of these three components underwent dramatic changes. Unfortunately, the validity of the formula has never been verified for these new conditions. Nobody proved so far that the formula is still valid for any other cutting tool materials than carbon steels and high speed steel (HSS). Moreover, one should clearly realize that tool life is not an absolute concept but depends on what is selected as the tool life criteria. In finishing operations, surface integrity and dimensional accuracy are of prime concern while in roughing operations, the excessive cutting force and chatter are limiting factors. In both, material removal rate and chip braking could be critical. These criteria, while important from the operational point of view, have little to do with the physical condition of the tool or physics of the cutting process. Analysis of the available criteria of tool wear and tool life assessment clearly indicates that these assessments are insufficient, very subjective and do not correlate with the tribology of metal cutting. They do not account for the tool geometry (the flank, rake, cutting edge angles, for example) so they are not suitable to compare cutting tools having different geometries. They do not account for the cutting regime and thus do not reflect the real amount of the work material removed by the tool during the time over which the measured flank wear is achieved. Finally, they are passive by nature because they are not correlated with the tribological conditions at the tool–chip and tool–workpiece interfaces so they can hardly be used for any process improvements and optimization as well as the process-adaptive intelligent control. Another way to look at the problem is to correlate tool wear with some tribological parameters at the tool–chip and tool–workpiece interfaces. To do that, the proper assessment of tool wear and its correlation with the tribological parameters at the mentioned interfaces should be established. In doing so, the influence of the geometrical and regime parameters of the cutting process and tool wear are established and explained. These are the objectives of this chapter. 4.3 Proper Assessment of Tool Wear To analyze the performance of cutting tools on CNC machines, production cells and lines, the dimension tool life, which is understood as the time period within the cutting

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225

tool that assures the required dimensional accuracy of the machined parts. The dimension tool life can be represented by: • The tool operating time (Top ). The operating time is understood as that time within which there is no dimension compensation or tool change due to tool wear. • The number of machined parts (Nmp ) during the tool operating time. • The overall length of tool path (LT ) during the tool operating time. • The overall area of the machined surface (Aop ) during the tool operating time. • Linear relative tool wear (hr−s ) during the tool operating time. All the listed characteristics of the dimension tool life are specific and thus, in general, are not suitable for the optimization of machining operations, comparison of various cutting regimes, assessments of various tool materials and so on. For example, it is not possible to compare two different tool materials if two different cutting speeds (suitable respectively for each one particularly) were used in the test. Therefore, the need is felt to introduce new characteristics for the dimension tool life [14]. Among suitable characteristics, the following seems to be the most reasonable: • Volumetric or mass tool wear is much versatile because it does not depend on tool geometry and design. This parameter can be measured directly. As such, the volume of lost tool material (Vw ) is obtained from the comparison of a 3D topography of the cutting wedge with that of the new tool (presumably stored in the memory of the image processing system). As such, the mass of worn material mw is calculated as, mw = ρct Vw ,

(4.2)

where ρct is the density of the tool material. Figure 4.2 shows wear curves when mw is used. Volumetric or mass tool wear can also be calculated using the results of linear measurements and parameters of tool geometry. Figure 4.4 shows some standard wear patterns and Table 4.1 presents the formulae to calculate the volumetric or mass characteristics of tool wear using the known tool geometry and the results of linear measurements [15]. • The dimension wear rate is the rate of shortening the cutting tip in the direction perpendicular to the machined surface taken within the normal wear period (region II in Fig. 4.2(b)), i.e νh =

hr − hr−i νfhs dνr νhl−r = = = dT T − Ti 1000 100

(µm/min) ,

(4.3)

where hr and hr−i are current and initial radial wear, respectively, T and Ti are the total and initial operating time, respectively and hs is the surface wear rate.

226

Tribology of Metal Cutting 90°-g

g VBB

b

x

a

VBB2

x

b

a

VBBX

VBB1

(a)

(b)

y

e b

b

x

x VBC

VBN

y x

y

(c) y

(d)

Fig. 4.4. Wear patterns to calculate volumetric wear.

Table 4.1. Formulas for calculating the volume and mass of material worn off the tool flank and rake. Figure 4.4(a)

Worn volume Vw =

Mass of worn material

bVB2B

sin α cos γ 2 cos (α + γ)

 Vw =

b

0

(VB2B1 + 2VBB1 cxn + c2 x2n )dx ,

2 cos (α + γ)

mw =

where VBB2 = VBB1 + cxn

4.4(c)

Vw =

sin α cos γ 2 cos (α + γ) 

VBc b tan−1 4.4(d)

Vw = 0

t1 VB2B sin α cos γ , 2 cos(α + γ) sin κr

where t1 is the depth of cut and κr is the cutting edge angle [5].

sin α cos γ 4.4(b)

mw = ρt

b/2  VBN − −b/2

ε

4VBN x2 b2

π (180 − ε) − 2 360 ε

4 cos 2

2 dx

 (VBc − y) dy

mw =

ρt b sin α cos γ · 2 cos (α + γ)   c2 b2n 2cVBB1 bn + b2 + n+1 2n + 1 4ρt bVB2N sin α cos γ 15 cos (α + γ)

 ε π (180 − ε)  ρt b2 VBC tan−1 − 2 360 ε

mw = 2 32 cos 2

Cutting Tool Wear, Tool Life and Cutting Tool Physical Resource

227

As it follows from Eq. (4.3), the dimension wear rate is inversely proportional to tool life but it does not depend on the selected wear criterion (a particular width of the flank wear land, for example). • The surface wear rate is the radial wear per 1000 sm2 of the machined area (S) hs =

µm/103 sm2 ,



(hr − hr−i ) 100 dhr = (l − li ) f dS

(4.4)

where hr−i and li are the initial radial wear and initial length of the tool path, respectively and l is the total length of the tool path. As it follows from Eq (4.4), the surface wear rate is reverse proportional to the overall machined area and, in contrast to it, does not depend on the selected wear criterion. • The specific dimension tool life is the area of the workpiece machined by the tool per 1 µm of its radial wear TUD =

(l − li ) f dS 1 = = (hr − hr−i ) 100 dhr hs



103 sm2 /µm .

(4.5)

The surface wear rate and the specific dimension tool life are versatile tool wear characteristics because they allow to compare different tool materials for different combinations of the cutting speeds and feeds using different criteria selected for assessment of tool life. Table 4.2 presents a comparison of different assessments of tool wear and thus the tool life. It is possible to use the width of the wear land at the tool point (nose) (current VBC and initial VBC−i ) instead of the radial wear (Fig. 4.1) to calculate the surface wear rate, i.e. hs =

(VBC − VBC−i ) 100 (l − li ) f

µm/103 sm2 .



(4.6)

Although such a substitution is correct, it is difficult to correlate VBC with the dimensional accuracy of machining. This is due to the plastic lowering of the cutting edge, which often occurs in machining difficult-to-machine materials. 4.4 Optimal Cutting Temperature – The First Metal Cutting Law 4.4.1 The essence of the first metal cutting law (the Makarow’s law) As discussed in Chapter 3, the cutting temperature is understood as the mean integral temperature at the tool–chip and tool–workpiece interfaces as measured by a tool-work thermocouple. As conclusively proven by Makarow [14], this temperature is the most suitable parameter to correlate the tribological conditions at the discussed interfaces with tool wear. Therefore, the correlation of this temperature with parameters of the cutting system should be established.

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Tribology of Metal Cutting

Characteristic

Designation/equation

Cutting speed (ν (m/min))

Cutting feed (f (mm/rev))

Dimensions of the machined part (surface)

Tool wear VBm or VBr

Possibility to use in calculations of dimension accuracy

Table 4.2. Comparison of different characterizations of tool life.

Machining time without adjustment or replacement of the tool (min) Number of part produced without adjustment or replacement of the tool Length of the tool path

Tc−l

+

+

−

+

No

Np−l

−

−

+

+

No

Lc−l = νTc−l

−

+

−

+

No

Area of the machined surface Volumetric or mass tool wear Linear relative wear

Ac−l = 10νTc−l f

−

−

−

+

No

mw

−

−

−

−

No

−

+

−

−

Yes

Dimension wear rate

νh =

+

+

−

−

Yes

Surface wear rate

h −h 100 hs = ( r (l−lr−i)f)

−

−

−

−

Yes

−

−

−

−

Yes

Specific dimensional tool life

Restriction factors

h −hr−i )1000 hl−r = ( r (l−l ) i

νhl−r 1000 i

TUD =

(l−li )f (hr −hr−i )100

Note that “+” means that the restrictive factors should be kept the same when using this characteristic for the comparison of cutting tools and regimes.

To do that, a simple factorial design of experiment (DOE) (discussed in detail in Chapter 5) can be employed. As the result of DOE, the following equation to correlate the cutting temperature, θct with parameters of the cutting regime for a given work material is obtained n

θct = Cθ νnν f nf dwd ,

(4.7)

where Cθ is constant that depends on the properties of the work material, nν , nf and nd are powers to be determined in DOE (Chapter 5). Table 4.3 shows the constants and powers obtained in machining different steels. As shown, the strongest influence on the cutting temperature has the cutting speed. Makarow showed [14] that the tougher the work materials (in terms of its machinability) gets, the stronger the influence of the cutting speed (compared to other machining parameters) becomes. Another important conclusion follows from the analysis of Eq. (4.7)

Cutting Tool Wear, Tool Life and Cutting Tool Physical Resource

229

Table 4.3. Coefficients and powers in Eq. (4.7). Tool material – P20, rake angle γ = 8◦ , flank angles of the major and minor cutting edges, α = α1 = 15◦ , tool cutting edge angle κr = 45◦ , tool cutting edge angle of the minor cutting edge κr1 = 15◦ . Work material

Cθ

nν

nf

nd

AISI AISI AISI AISI AISI

228 269 352 224 326

0.25 0.27 0.22 0.33 0.28

0.07 0.15 0.08 0.11 0.12

0.03 0.10 0.05 0.07 0.07

1010 1020 1045 1080 07

and Table 4.3, namely that the same cutting temperature can be achieved using different combinations of the terms of Eq. (4.7). Analyzing a great body of experimental data, Makarow formulated the law [14] which was presented as the First Metal Cutting Law (the Makarow’s law) by Astakhov [16,17]:

For given combination of the tool and work materials, there is the cutting temperature, referred to as the optimal cutting temperature θopt , at which the combination of minimum tool wear rate, minimum stabilized cutting force, and highest quality of the machined surface is achieved. This temperature is invariant to the way it has been achieved (whether the workpiece was cooled, pre-heated etc.).

The first metal cutting law, established initially for longitudinal turning of various work materials (example is shown in Fig. 4.5(a), was then experimentally proven for various machining operations. Figure 4.5(b) shows its applicability in twist drilling, Fig. 4.5(c) – in thread cutting, Fig. 4.5(d) – in gear hobbing. Considering Fig. 4.5(a), one can see that when the cutting feed increases, the surface wear rate reduces. However, minimum tool wear rates, when various cutting feed are used, occur at the same optimal cutting temperature θopt , although the amount of the surface wear rate varies more than 2 times. Even more pronounced effect can be observed in Fig. 4.5(b), where the cutting feed has a much stronger influence on tool life, represented by the total length of the tool path to achieve VBB = 0.3 mm. As shown, there is a specific combination of the cutting speed and feed at which tool life is at a maximum. Changing the cutting speed and/or feed on either side reduces tool life while the minimum tool wear rate under a given combination of these parameters corresponds to the optimal cutting temperature. Figure 4.5(c) shows that tool life in thread cutting, represented by the total length of the tool path (L (m)) to achieve VBB = 0.5 mm, has its maximum at the same optimal cutting temperature, θopt under different combinations of cutting speed and feeds. Figure 4.5(d) shows that the same conclusion can be drawn from the data for gear hobbing. Figure 4.6 shows that the machining at optimal cutting temperature results not only at the minimum tool wear rate but also leads to obtaining the minimum cutting force and smallest roughness of the machined surface. As it follows from this picture, under

230

Tribology of Metal Cutting

hs (µm/103 sm2)

q(°C) 1

2

qopt

L (mm)

3

4

7

500

400 120

300

5

5

3

qopt

800 160

700

2

1 5

9

q (°C)

1200

3

80

3

2

4

3

40

2

1

1

0

1 0

40

80

120

160

(a)

L (m)

n (m/min) q(°C)

0

4

N (pc)

n (m/min) q (°C)

qopt 700

18

600

1

14

200

2

3

2

300

2

1

2

1

16

400

3

250

150

12

(b)

800

qopt

200

8

1

10 3

6

100 3

40 30

2 50

70

90

(c)

110

n (m/min)

0

10

20

30

n (m/min)

(d)

Fig. 4.5. Optimal cutting temperature: (a) turning, tool material – P30, work material – AISI 1045, depth of cut dw = 1.5 mm using different cutting feeds: 1 – 1.4, 2 – 0.87, 3 – 0.61, 4 – 0.39 and 5 – 0.39 mm/rev, (b) drilling with twist drills, tool material – HSS T15, work material – AL 610 alloy, drill diameter – 15 mm, tool life criterion – VBB = 0.3 mm using different feeds: 1 – 0.28, 2 – 0.17 and 3 – 0.10 mm/rev, (c) thread cutting with a single-point cutting tool, tool material – M10, work material – AISI 303, tool life criterion – VBB = 0.5 mm, using different feeds: 1 – 1.0, 2 – 1.5 and 3 – 2.0 mm/rev, (d) gear hobbing, tool material – HSS T15, work material – AISI 4140, module, m = 2 mm, number of teeth z = 61, VBB = 0.7 mm, using different axial feeds: 1 – 4.0, 2 – 2.5 and 3 – 1.7 mm/rev.

given cutting conditions, the optimal cutting temperature θopt = 875◦ C can be directly correlated to the so-called optimal cutting speed νopt = 1.28 m/s. To understand the technical and physical background of the optimal cutting temperature, one should understand what happens with the work material at this temperature. Figure 4.7 presents the answers to this question at the technical level. This figure shows what happens with the most relevant (to machining) mechanical characteristics of the work material when this material is brought to the temperature equal to the optimal

Cutting Tool Wear, Tool Life and Cutting Tool Physical Resource hs

µm 0.1m2 11

Rz

Fz

µm

N

25

700

23

600

231 θ(°C)

Fz 1100 Rz

9

900 qopt = 875°C

hs

7

21

500

700

5

19

400

500

2

17

300

q 200 Vopt = 1.28m/s

0

0.4

0.8

1.2

1.6

2.0

2.4

n (m/s)

Fig. 4.6. Experimental determination of the optimum cutting speed and temperature using longitudinal turning of AISI 4340 steel. Tool material: carbide P20. Cutting regime: f = 0.15 mm/rev, dw =1 mm.

cutting temperature. Particularly, the minima of the ultimate strength, σUTS and elongation, ef (which represents the strain at fracture) result in the minimum work done in the fracture of the layer being removed as discussed in Chapter 2. The minimum microhardness, HV assures the minimum of the normal stress at the tool–chip interface as discussed in Chapter 3. The minimum Young’s modulus assures the minimum work of elastic deformation (Chapter 2) while the minimum of hr−s results in minimum tool flank wear. To understand the discussed phenomena at the level of physical metallurgy, one should recognize that metal cutting is the purposeful fracture of the work material as defined by Astakhov [16]. As discussed in Chapter 2, the work spent in purposeful fracturing of the layer being removed, i.e. its fracture toughness, should be considered as the prime parameter in determining the cutting force and the energy spent in machining. Therefore, one should consider the mechanics of fracture [18] and the importance of the process temperature in this mechanics. Another important aspect of metal cutting, discussed in Chapter 2, is plastic deformation that should be considered as a waste of energy. In metal cutting, it is desired that the work materials have as small a strain at fracture as possible. According to Atkins and Mai [18] and Komarovsky and Astakhov [19], there is a marked increase in the strain at fracture and also in the work of fracture, at about 0.18–0.25 of the melting point (Tm ); similar changes occur in other measurements of ductility such as Charpy values (CVN), as shown in Fig. 4.8(a). It explains a number of “strange” results obtained by Zorev in his tests at low cutting speeds [20]. This phenomenon also explains the great size of the zone of plastic deformation observed at low cutting speeds, and incorporated in the model discussed by Astakhov [16]. The known built-up edge

232

Tribology of Metal Cutting

hrs (µm/km)

80

60

40

20

E (GPa)

180 140 100 90

ef (%)

70

50

30

10

HV (MPa)

180 140 100

suts (MPa)

350 250 150 600

800

θopt 1000

1200

Temperature (°C) Fig. 4.7. Influence of temperature on the properties of pure iron.

Cutting Tool Wear, Tool Life and Cutting Tool Physical Resource

233

C

A

Voids

Ductility

B notch

D

(a)

voids particles

0

(0°K)

0.1

0.2

0.3

Temperature, T/Tm DIFFUSION IMPORTANT

C

D

E

g

in

id

Sl

Voids

Ductility

Cavities

0.3 Room Temp

0.4

0.5

Recrystallisation Partial Full

(b)

0.6

Temperature, T/Tm

Fig. 4.8. Changes in ductility and typical associated mechanisms of fracture for bss materials: (a) at temperatures <0.3 Tm : (A) low-temperature intergranular cracks, (B) twinning or slip leading to cleavage, (C) shear fracture at particles, (D) low energy shear at particles; (b) at temperatures >0.3 Tm : (C) shear at particles, (D) cavities along grain faces, (E) recrystallization suppresses cavitation.

is the result of the discussed high plasticity region in front of the tool rake face within the contact length. Exceptions are certain fcc metals and alloys (Al, Cu, Ni, Pb) that do not normally cleave. As such, there is no transition in values, which gradually rises with temperature. The increase in ductility over the “transition temperature range” is followed by a gradual drop beyond approximately 0.35 Tm . It is believed that it happens due to the continuous fall in the Peierls–Nabarro stress which opposes dislocation movement, coupled with the emergence of cross-slip (as opposed to Frank–Read sources) as a dislocation generator as the temperature is raised [18]. In the author’s opinion the cause is in dilation–compression reactions as explained in Ref. [19].

234

Tribology of Metal Cutting

At high temperatures, grain boundaries become significant. Below approximately 0.45 Tm grain boundaries act principally as barriers inhibiting cleavage and causing dislocation pile-ups. At higher temperatures, the regions of intense deformation, which are contained within the grains at lower temperatures, now shift to the grain boundaries themselves. Voids are nucleated and then cracks develop on the grain boundaries. Shear stresses on the boundaries cause relative sliding of the grains, and voids are reduced in the region of stress concentrations (see Fig. 4.8(b) – position D). Therefore, the region around this temperature can be termed as the ductility valley. Experiments showed [14] that the reduction of plasticity may reach two fold and even more for high alloys. The presence of this valley is the physical cause of the existence of the optimal cutting temperature. At temperatures (0.5–0.6) Tm , recovery and re-crystallization processes set in (recovery relates to a re-distribution of dislocation sources so that dislocation movement is easier, and in re-crystallization, the energy of dislocations generated during prior deformation is used to nucleate and grow new grains, thus effecting annealed structure over a long time). The net effect is increased ductility causing a bump shown in Fig. 4.8(b).

4.4.2 Major consequences of the first metal cutting law (Makarow’s law) The following consequences of the first metal cutting law are of great importance in the tribology of metal cutting. Consequence 1: For cutting tools with various combinations of cutting geometry parameters (Appendix A) – rake, flank, inclination, tool cutting edge angles, nose and cutting edge radii, etc. – the optimal cutting temperature corresponds to the points of minimum on the curves representing the dependence of tool wear rate on the cutting speed while the optimal cutting speed corresponding to each and every particular case varies in a wide range. Figure 4.9(a) and Table 4.4 show an example of experimental verification of this consequence. Consequence 2: The minimum tool wear rate is achieved at the same optimal temperature in dry cutting and in cutting with various cutting fluids (media) using various methods of cutting fluid supply. Figure 4.9(b) demonstrates an example of the obtained experimental data. As shown, the optimal temperature is the same for dry machining as well as for machining using different cutting fluids. Consequence 3: The optimal cutting temperature is the same for various combinations of the temperature of the preheated workpiece and uncut chip thicknesses. This is illustrated by an example shown in Fig. 4.9(c) and Table 4.5. In other words, the optimal cutting temperature does not depend on or is invariant to a particular method by which it was achieved. Consequence 4: Variation of the workpiece diameter in turning and boring leads to a significant change in the optimal cutting speed (i.e. the cutting speed corresponding to the minimum tool wear rate). The reason for this is discussed in Chapter 2, where the interactions of the deformation and thermal waves are considered. The optimal

Cutting Tool Wear, Tool Life and Cutting Tool Physical Resource

hs (µm/103 sm2)

hs (µm/103 sm2)

q(°C) 2 3

1

q (°C) 1000

qopt 800

30

qopt 800

235

1

600

400

1 3

2

200

20 4

2

400

5

10

6

600

3

0 hs

(µm/103

20

40

60

n (m/min)

(b)

sm2)

q (°C) 1200

400 2

4

5

5

800

800

qopt

1

600 3

200 4

0

400

1

200

0

400 5

2

3

40

80

120

n (m/min)

(a)

1

3 2 4

0

10

20

30

n (m/min)

40

(c) Fig. 4.9. Influence of cutting speed on the cutting temperature and tool wear rate: (a) wear in turning AL 610 alloy, tool material – carbide P10 (14% TiC, 8% Co), combinations of the tool geometry parameters are shown in Table 4.4, (b) wear in turning Haynes 263 alloy (29% Cr, 2.5% Ti), tool material – carbide M20 (92% WC, 8% Co), depth of cut dw = 0.5 mm, cutting feed f = 0.08 mm/rev, curves: (1) dry cutting, (2) water-based (6%) cutting fluid, (3) oil-based cutting fluid with chlorine and sulfur, (c) wear in turning Haynes 263 alloy with pre-heating of the workpiece, tool material – carbide M10 (92% WC, 8% Co), depth of cut dw = 0.5 mm, feeds and pre-heating temperatures are shown in Table 4.5.

Table 4.4. Regime and geometry parameters in Fig. 4.9(a). Curve No. 1 2 3 4 5 6

dw (mm)

f (mm/rev)

0.5

α (◦ )

γ (◦ )

10 0.09

0.25 0.18

10

κr (◦ ) 45 90

16 10

30 10

45

λp ( ◦ ) −10 0

rn (mm) 0.3 0.1 1.0 0.1 1.0

236

Tribology of Metal Cutting Table 4.5. Parameters of curves in Fig. 4.9(c). Curve No.

f (mm/rev)

θph (◦ C)

0.11 0.21 0.3 0.11 0.3

20 100 200 300 300

1 2 3 4 5

temperature, however, remains the same. This is illustrated by an example shown in Fig. 4.10. Consequence 5: If the structure and/or hardness of the work material are changed, the optimal cutting speed is changed correspondingly, but the optimal temperature, remains the same. This is illustrated by an example shown in Figs. 4.11(a) and (b) where the test results for turning using the same high-carbon tool steel brought to different hardness are shown. As shown, the optimal cutting speed changes with the hardness and metallurgical structure of the work material (Fig. 4.11(a)) while the optimal cutting temperature remains the same (Fig. 4.11(b)). The summary of the considered consequences is as follows: The optimal cutting temperature depends upon only the compositions of the tool and work materials, so it can be determined once, and then used to optimize various cutting processes where the same combination of tool/work materials is used. This temperature does not depend on the type of cutting operation, tool geometry, parameters of machining regime, particular type and method of application of the cutting fluid, etc.

q (°C) 1000 L (m)

800

θopt

600

300 Dw = 90mm

200 45mm

100 27mm

0

20

40

60

n (m/min)

Fig. 4.10. Influence of cutting speed on the cutting temperature and the total length of the tool path in machining workpiece of three different diameters in turning. Work material – Haynes 263 alloy (29% Cr, 2.5% Ti), tool material – micrograin carbide M10 (94% WC, 6% Co), depth of cut dw = 0.25 mm, cutting feed f = 0.09 mm/rev, tool life criterion – radial tool wear VBr = 30 µm.

Cutting Tool Wear, Tool Life and Cutting Tool Physical Resource hs (µm/103 sm2)

237

hs (µm/103 sm2)

800

800

600

600 HRC65

HRC65

400

400

300

300 200

200 HRC55

HRC55 100

100

80

80

60

60 HRC45

HRC45 40

40

30 8

12

20

30 40

60 n (m/min)

30 400

(a)

600

800 q (°C)

(b)

Fig. 4.11. Influence of cutting speed (a) and cutting temperature (b) on tool wear rate in turning of tool steel HVG (1% C, 1% Cr, 1.5% W, 1% Mn). Tool material – carbide M20 (92% WC, 8% Co), depth of cut dw = 0.25 mm and cutting feed f = 0.10 mm/rev.

4.4.3 Methods of determining the optimal cutting temperature The optimal cutting temperature can be determined experimentally using a tool-life test, where the tool wear rate hs is measured as a function of the cutting temperature. The temperature corresponding to the minimum tool wear rate is considered as the optimal cutting temperature. However, a complete tool life test is expensive and time consuming although it has to be carried out only once for a given combination of the work and tool materials. It has been suggested, therefore, that such a test be conducted at a constant depth of cut and cutting feed, varying the cutting speed and measuring tool wear rate hs . As it follows from the data shown in Fig. 4.6, the cutting force and surface finish can also be measured to establish the optimal cutting temperature. As shown in this figure, the optimal cutting temperature was determined to be 875◦ C. Conducting a number of tests with difficult-to-machine materials, Silin [21] showed that the optimal cutting temperature can be determined as corresponding to the minimum stabilized cutting force, as shown in Fig. 4.12. As shown, the optimal cutting temperature does not depend on a particular cutting regime. The optimal cutting temperature can also be determined if the correlation curves of the “temperature–hardness” are known for the work and tool materials. As such, the optimal

238

Tribology of Metal Cutting

q (°C)

6 7

5 4

3

800 1

2 700

600

500 400 Fz (N) 1600

7 6

1200

5 4 3

1000

2 1 400

0

0.1

0.2

0.3

0.4

0.5

0.6

n (m/s)

Fig. 4.12. Experimental determination of the optimal cutting temperature by the minimum stabilized cutting force. Workpiece materials: nickel-based alloy (0.08% C, 1% Cr, 56% Ni, 1% Co, 1% Al), tool material – carbide M20 (92% WC, 8% Co), tool geometry: γ = 12◦ , α = 12◦ , κr = 45◦ , κr1 = 45◦ , rn = 1 mm, depth of cut dw = 1.0 mm, cutting feeds as corresponding to curves: (1) f = 0.074, (2) 0.11, (3) 0.15, (4) 0.25, (5) 0.30, (6) 0.34 and (7) 0.39 mm/rev.

cutting temperature is determined as the temperature corresponding to the maximum difference of these hardnesses, as shown in Fig. 4.13. Conducting a similarity study of metal cutting parameters, Silin suggested the following theoretical equation for determining the optimal cutting temperature for carbide tools [21]  θopt = 0.6 Tmp−c

kct kw

0.13 

CP−w ρw CP−cf ρct



m0.27 0.05 , 1 + ef



(4.8)

where Tmp−c is the melting temperature of cobalt, Tmp−c = 1490◦ C, kct and kw are thermoconductivities of the tool and work materials, respectively, CP−ct and CP−w

Cutting Tool Wear, Tool Life and Cutting Tool Physical Resource

HV

239

Ht = f(q )

Hw = f(q )

Ht = f(q ) Hw

qopt

q

Fig. 4.13. Determination of the optimal cutting temperature using temperature–hardness curves.

Table 4.6. Coefficient m in Eq. (4.8). Group of work materials Carbon steels Chromium and tool steels Chromium–molybdenum and chromium–tungsten steels Stainless and heat-resistant steels

Group of work materials

m 0.925 0.800 0.970

Nickel-based heat-resistant steels Titanium alloys Aluminum high alloys

1.300

Copper, brass Bronze

m 1.100 0.6–0.7 0.95 1.25 1.05

are specific heats of the tool and work materials, respectively, ρct and ρw are the densities of the tool and work materials, respectively, ef is the elongation at fracture of the work material and m is a coefficient in Table 4.6. 4.5 Influence of Cutting Feed and Depth of Cut 4.5.1 Influence of cutting feed in a wide range of cutting parameters The uncut chip thickness or the cutting feed has direct influence of the quality, productivity and efficiency of machining. It is believed that tool life decreases (and thus tool wear increases) with the cutting feed [5,20,22,23]. Such a perception is based on a generally adopted equation for tool life. For example, generalizing experimental data, Gorczyca proposed (Eq. (5.9) in [23]) the following equation, T =

48.36 × 106 ν4 f 1.6 dw0.48

(4.9)

240

Tribology of Metal Cutting

As shown, if the cutting speed ν = constant and the depth of cut dw = constant, then the tool life increases when the cutting feed decreases and vice versa. A great body of data to support the discussed point and thus the structure of Eq. (4.9) can be found in the literature on metal cutting, although some researches starting with Taylor [13] did not include the cutting feed in tool life equations because this parameter was not considered as having a significant influence on tool life while others found that the experimentally obtained relation hs = (f ) has a distinctive minimum. Such a great scatter in the experimental results can be explained by the fact that the cutting tests were carried out under invariable cutting speeds that resulted in different cutting temperatures when the cutting feed was varied. To gain an understanding of the true influence of the cutting feed on tool wear, this influence should be considered in the context of other parameters of the cutting process that make contributions to the cutting temperature. As such, the influence of the cutting feed (the uncut chip thickness) on the surface wear is of prime interest while keeping the area of the machined surface constant (or the volume of the removed work material) in contrast to the length of the cutting path. This is because the area of the machined surface (or the volume of the removed work material) does not change with the cutting feed while the length of the tool path does. Studying the influence of the cutting feed on the surface wear, Makarow [14] considered the following factors, Factor 1: When cutting feed increases (and ν = constant), the length of the tool path decreases if the machined area is kept constant. As a result, the cutting (contact) time as well as the tool wear rate decreases. Therefore, the surface wear rate decreases. Factor 2: Any change in the cutting feed leads to the corresponding change in the cutting temperature, so the cutting feed should influence the tool wear rate. As such, there are three basic scenarios: (a) if the current machining takes place using relatively low cutting speed so that the cutting temperature is lower than the optimal cutting temperature, then an increase in the cutting feed leads to a decrease in the tool wear rate, (b) if the current machining takes place using an “average” cutting speed so that the cutting temperature passes its optimum with an increase in the cutting feed, then the relation hs = (f ) has a distinctive minimum. In other words, increasing the cutting feed until the cutting temperature remains below the optimal cutting temperature reduces the tool wear rate while any further increase would increase this wear rate, (c) if the current machining takes place using a high cutting speed, i.e. when the cutting temperature is higher than the optimal cutting temperature, then any increase in the cutting feed should lead to an increase in the tool wear rate. Factor 3: The tool actually cuts the transient surface (the surface being cut by the major cutting edge, see Appendix A). Because in most practical machining operations the tool cuts part of the transient surface formed on the previous tool pass, the amount of cold working imposed by this tool on the previous pass affects the cutting conditions on the current pass. Among other characteristics, the depth of cold working (dcw ) with respect to the uncut chip thickness (t1 ) is of prime concern. When the cutting feed (the uncut chip

Cutting Tool Wear, Tool Life and Cutting Tool Physical Resource

241

thickness) is small then it can so happen that dcw > t1 and the major cutting edge cuts the cold worked work material characterized by a greater strength and hardness compared to those of the original work material. As such, the tool wear rate increases. If this is the case, one increases the cutting feed so that the uncut chip thickness becomes greater than dcw , the tool wear rate decreases. Factor 4: As discussed in Chapter 3, increasing the cutting feed leads to the corresponding increase in the normal contact stress at the tool–chip interface and in the tool–chip contact area (length). However, the contact area increases in a much smaller rate compared to the normal contact stress [14]. When the level of the normal contact stress reaches a certain tool-material specific limit, the chipping of the cutting edge takes place that eventually leads to tool breakage. Such a limit can be referred to as the breaking feed. Normally, the cutting feed used in machining common work materials is below the breaking feed as the this feed is limited by the requirements to the surface integrity and power of the feed drive. However, in hard turning, the operation that attracts more and more attention in the automotive and aerospace industries, the breaking feed is normally well below those allowed by the surface finish of machined parts and by the power of the feed drive used, so that the working cutting feed can be in close proximity to the breaking feed. Factor 5: Often, the intensity of vibrations that take place in machining reduces with the cutting feed. When it happens, the tool wear rate reduces. Moreover, increasing the cutting feed changes the ratio of the radial, Fy and the axial (feed), Fx forces (Fig. A1.5) that increases the dynamic rigidity of the machine tool. Summarizing the above considerations, one should realize that when the cutting feed increases, the cumulative effect of the discussed factors may affect the tool wear rate in considerably different ways depending upon many parameters and characteristics of a particular cutting system. Makarow [14] found that the effect of the cutting feed becomes more apparent with difficult-to-machine work materials having a great number of alloying components. As an example, consider the influence of the cutting feed on the surface wear rate, hs in machining AL 610 alloy. AL 610 is a low-carbon (less than 0.015 wt.%), silicon-containing (up to 4.3 wt.% Si), chromium (up to 18.5 wt.% Cr), nickel (up to 15.5 wt.% Ni) austenitic stainless steel. This alloy is typically used for applications in the chemical industry. The high silicon content provides very good resistance to oxidizing environments, such as concentrated nitric acid, over a wide range of temperatures. In the tests, the feed rate was selected to be in the range of 0.2–0.4 mm/rev. As such, the uncut chip thickness is greater than the depth of cold working, there were no noticeable vibrations, no chipping of the cutting edge and tool breakages so Factors 3–5 did not affect the tool wear rate as the cutting feed was increased. Therefore, the relation hs = (f ) was determined only by Factors 1 and 2. Factor 1 always reduces the tool wear rate with increasing the cutting feed. To study the influence of Factor 2, the cutting temperature was determined as a function

242

Tribology of Metal Cutting hs (µm/103 sm2) a1 a2

n=75m/min

f =0.20mm/rev

90 n =160m/min 70 n =130m/min 50

c3 c1

f =0.30mm/rev

c2

b2

b1 a3

b3

f =0.40mm/rev

30 10 750

qopt 800

850

900

950

1000

1050

1100

qc(°C)

Fig. 4.14. The influence of cutting temperature on the tool wear rate in turning AL 610 alloy. Tool material – carbide P10 (14% TiC, 8% Co). Depth of cut dw = 1 mm.

of the cutting regime. The result is shown in Fig. 4.14. The different cutting temperatures were obtained by variation of the cutting speed. Consider the change in the cutting temperature and tool wear rate when the cutting feed changes from 0.2 to 0.4 mm/rev at three different cutting speeds, 75, 130 and 160 m/min. As shown in Fig. 4.14, when the cutting feed increases in a zone where the resulting cutting temperature is less than θopt , this increase leads to the reduction of the tool wear rate. If the opposite happens, then the cutting temperature exceeds θopt . When the cutting speed is ν = 75 m/min, an increase in the feed from 0.2 to 0.4 mm/rev leads to the increase in the cutting temperature within the left branch of curve hs = (f ). As such, the higher the cutting feed, the higher the cutting temperature and the lower the tool wear rate (points a1 , a2 and a3 ). Therefore, Factors 1 and 2 reduce the tool wear rate with increasing the cutting feed. When the cutting speed is ν = 130 m/min, increasing the feed from 0.2 to 0.4 mm/rev causes the cutting temperature to pass its optimum. As such, an increase of the cutting feed from 0.2 to 0.3 mm/rev leads to an increase in the cutting temperature and reduction of the tool wear rate while the increase of the cutting feed from 0.3 to 0.4 mm/rev leads to the increase of the tool wear rate (points b1 , b2 and b3 ). In the latter transition, Factors 1 and 2 work simultaneously but in an opposite manner in terms of their influence on the tool wear rate. The influence of Factor 2 is stronger that causes an increase in tool wear rate. When the cutting speed is ν = 160 m/min, any increase of the cutting feed leads to an increase of the tool wear rate. Points c1 , c2 and c3 (Fig. 4.14) show what happens when the cutting feed increases from 0.2 to 0.3 mm/rev and then to 0.4 mm/rev, respectively. As it follows from the above consideration, the influence of the cutting feed on the tool wear rate is different at different cutting speeds. In the considered case, the major factor affecting tool wear rate is the cutting temperature.

Cutting Tool Wear, Tool Life and Cutting Tool Physical Resource

243

Factor 3 is extremely important but practically always ignored in metal cutting theory and practice. As discussed above, the tool actually cuts the transient surface (the surface being cut by the major cutting edge, see Appendix A). Because in most practical machining operations, the tool cuts the part of the transient surface formed on the previous tool pass, the amount of cold working imposed by this tool on the previous pass affect the cutting conditions on the current pass. As mentioned, the depth of cold working (dcw ) with respect to the uncut chip thickness (t1 ) is of prime concern (Fig. 4.15(a)). This is particularly important when cutting at low feeds, i.e. when the uncut chip thickness is smaller than the depth of cold working, i.e. when dcv > t1 . When it happens, the major cutting edge cuts the cold worked work material characterized by greater strength and hardness. As such, the tool wear rate increases. Figure 4.15(b) illustrates this point. When the feed is 0.1 mm/rev, the depth of cold working is greater than the uncut chip thickness so the cutting wedge cuts the cold worked work material that results in a greater tool wear rate. In the feed range of 0.1–0.2 mm/rev, the influence of Factor 1 leads to the reduction of the tool wear rate. When the feed increases further, the influence of Factor 2 becomes predominant that increases the tool wear rate.

4.5.2 Influence of cutting feed under the optimal cutting temperature Understanding influence of the cutting feed under the optimal cutting temperature is important in the selection of the optimal cutting regime since the optimal combination of cutting speeds and feeds should be used in the practice of metal cutting.

Transient surface

hs (µm/103 sm2)

f 6 n =120m/min 4 n =90m/min

2

dcw

0 0.1

t1

(a)

n =60m/min 0.2

0.3

f (mm/rev)

(b)

Fig. 4.15. Depth of coldworking of the transient surface: (a) model, (b) influence of the feed on tool wear rate. Work material – stainless steel AISI 303, tool material – carbide M10 (97% WC, 3% Co), depth of cut dw = 0.5 mm.

244

Tribology of Metal Cutting

Makarow [14] proved that the correlation between the optimal cutting speed and feed as well as between the optimal wear rate and feed can be established as, νopt =

Cν , f xν

(4.10)

hs−opt =

Ch , f xh

(4.11)

where Cν and Ch are constants determined by the properties of the work material, xν , xh are the powers determined by the specifics of the machining operation. The dimension tool life TD can be represented as the product of the tool radial wear (hr ) and the specific dimension tool life (TUD )

TD = hr TUD × 103 sm2 .

(4.12)

As discussed above, the lower the wear rate (hs ), the higher the specific dimension tool life, the greater number of parts can be machined without correction/compensation of the tool. The specific dimension tool life corresponding to the optimal surface wear can be referred to as the optimal specific dimension tool life (TUD−o ). Therefore, the optimal tool life can be represented as TD−o = hr TUD−o =

hr hr xh = f x Ch /f h Ch

(4.13)

Because Ch = constant then, when hr = constant, the dimension tool life is proportional to power xh . This power is in the range of 0.31–0.75 and is always positive. Therefore, in machining, if the optimal temperature is kept constant, an increase in the cutting feed leads to an increase in the dimension tool life. The greater the xh , the stronger the influence of the feed on the dimension tool life, and the greater the increase of the dimension tool life with the cutting feed. For example, a fourfold increase in the cutting feed (from 0.1 to 0.4 mm/rev) in turning stainless steel AISI 303 using M20 (94% WC, 6% Co) carbide tool (power xh = 1.3) led to the increase in the dimension tool life by 6.2 times while a 3.28-time increase was achieved in the same operation when P10 (30% TiC, 66% WC, 4% Co) tool was used (power xh = 0.88 ) [14].

4.5.3 Influence of depth of cut When the depth of cut increases and the uncut chip thickness is kept the same, the specific contact stresses at the tool–chip interfaces, chip compression ratio and average contact temperature remain unchanged. Therefore, an increase in the depth of cut should not change the tool wear rate if the machining is carried out at the optimum cutting regime.

Cutting Tool Wear, Tool Life and Cutting Tool Physical Resource hs (µm/103 sm2)

245

hs (µm/103 sm2) f=0.10 mm/rev

4

80 f=0.12 mm/rev f=0.20 mm/rev

2

f=0.23 mm/rev

40 f=0.47 mm/rev

0 0.5

f =0.40 mm/rev

1.0

1.5

0

dw(mm)

0.5

(a)

1.0

1.5

dw(mm)

(b)

Fig. 4.16. Influence of depth of cut on the tool wear rate: (a) cutting with the invariable cutting speed optimal for dw = 0.5 mm, work material – stainless steel AISI 303, tool material – carbide M10 ((97% WC, 3% Co), (b) cutting with the invariable optimal cutting temperature determined for dw = 1.0 mm, work material – AL 610 alloy, tool material – carbide M20 (92% WC, 8% Co).

Figure 4.16(a) shows the influence of the depth of cut on the tool wear rate. In the test, the cutting speed was determined to be optimal for the depth of cut dw = 0.5 mm and was kept invariable for the other depth of cut. As shown, the depth of cut has very little influence on the tool wear rate. In another series of tests, the optimal cutting temperature determined for dw = 1.0 mm was kept invariable in the test. The test results are shown in Fig. 4.16(b). As shown, the depth of cut has little influence on the tool wear rate.

4.6 Influence of Tool Geometry The tool geometry and significance of its components are discussed in Appendix A. It is shown that the uncut chip thickness is an important parameter in metal cutting and it directly correlates with tool geometry. The influence of the tool nose radius on the uncut chip thickness is also discussed and the shape of the uncut chip is correlated with this radius and other geometrical parameters of the cutting tool. The shape, mean uncut chip thickness and width as well as the cutting temperature are greatly affected by the tool nose radius, rn . Therefore, this radius should significantly affect the shape of curves hs−o = f(ν). Figure 4.17(a) presents an experimental support to this point. For the considered case, the following empirical equation is valid. νopt = 23.2rn0.25 .

(4.14)

When cutting with low cutting speeds (ν = 16 m/min), tool wear rate increases significantly with the nose radius, as shown in Fig. 4.17(b). The change of this radius from  rn = 0.5 to 4 mm led to the increase of tool wear rate hs from 32 to 120 µm/ 103 × sm2 ,

246

Tribology of Metal Cutting θ(°C)

θ(°C)

1.0 mm n=40 m/min

900

850

2.0 mm

0.5 mm

850

qopt

800

25 m/min

800

4.0 mm

qopt

hs

750 700

hs

3 2 750 (µm/10 sm )

(µm/103 sm2)

900

650 16 m/min

600

120

700

100

0.5 mm

100

80

1.0 mm

80

40 m/min

2.0 mm

16 m/min

60

60 40

40

rn=4.0 mm

20 10

20

30

40

(a)

50

60 n (m/min)

25 m/min

20 0

1

2

3

4 rn(mm)

(b)

Fig. 4.17. Influence of cutting speed on the tool wear rate and cutting temperature in turning. Work material – Haynes 263 alloy (29% Cr, 2.5% Ti), tool material – micrograin carbide M10 (94% WC, 6% Co) depth of cut dw = 1 mm, cutting feed f = 0.20 mm/rev: (a) for different tool nose radii and (b) influence of the nose radius.

i.e. by four times. This is because the cutting temperature decreases with the nose radius, so it departures further from the optimal cutting temperature when the nose radius increases. When cutting with moderate cutting speeds (ν = 25 m/min), the tool wear rate first decreases with the nose radius and after reaching a certain minimum, then increases. This is because the cutting temperature first decreases and approaches the optimal cutting temperature at which the tool wear rate is minimum. Further increase in the nose radius leads to further decrease in the cutting temperature. As this temperature departs from the optimal cutting temperature, the tool wear rate increases. When cutting with high cutting speeds (ν = 40 m/min), the tool wear rate decreases monotonely and continuously increases with the nose radius. This is because the cutting temperature decreases, thus approaching the optimal cutting temperature. The tool cutting edge angle (κr ) affects the uncut chip thickness, its width as well as the cutting temperature. Conducting a great number of cutting tests, Makarow found [14] that relationships hs−o = f(ν) have different minima at various tool cutting edge angles although the optimal cutting temperature does not change. For example, in turning AL 610 alloy using carbide M20 (92% WC, 8% Co), depth of cut dw = 0.25 mm, feed f = 0.09 mm/rev and tool nose radius rn = 0.10 mm, the optimal cutting speed

Cutting Tool Wear, Tool Life and Cutting Tool Physical Resource

247

and the tool cutting edge angle correlate as follows: νopt =

248 . κr0.33

(4.15)

As for the tool cutting edge angle of the minor cutting edge (κr1 ), it was found that being varied in the practically used range of 5–45◦ , this angle has negligibly small influence on the optimal cutting speed and tool wear rate. The influence of the rake angle is estimated using the so-called angle of cut which is calculated as the sum of the flank angle and the angle of the cutting wedge (Appendix A) δct = α + β

(4.16)

When the angle of cut δct increases, the deformation of chip, friction losses at the tool–chip interface, and cutting temperature increase correspondingly. Therefore, when δct increases, the optimal cutting speed decreases, so the optimal cutting temperature remains invariable. For example, in turning AL 610 alloy using carbide M20 (92% WC, 8% Co), depth of cut dw = 0.25 mm, feed f = 0.09 mm/rev, the optimal cutting speed and the angle of cut δct correlate as follows: νopt =

992 . δ0.60 ct

(4.17)

The cutting edge inclination angle (λs ) defines the orientation of the tool rake face with respect to the cutting speed vector. As a result, the optimal cutting speed changes while the optimal temperature remains invariable. The influence of the inclination angle, however, is extremely complex because it depends on many other parameters of the cutting system and properties (both mechanical and physical) of the work material. As discussed in the previous chapter, the inclination angle is the major contributor to the formation of the state of stress in the layer being removed on the one hand, and on the other, affects significantly the tribological processes at the tool–chip interface. Therefore, it is impossible to determine the net influence of this angle on the tool wear rate at this stage. Although the flank angle (α) does not affect the cutting temperature directly, it does affect the dimension wear rate. This rate increases when the flank angle increases. When the cutting speed is kept invariable, it can be correlated with the flank angle as, hs = Cα α0.40 .

(4.18)

The independence of the optimal cutting temperature on the parameters of tool geometry allows to determine the optimal cutting speed for any given tool geometry parameters using a simple cutting test, where the relationship hs−o = f(ν) determined for an invariable uncut chip cross-sectional area. Having conducted tests for other combinations

248

Tribology of Metal Cutting

of the tool geometry parameters and determining dependences θ = f(ν) and e.m.f. = f(ν) for these combinations, one can determine the optimal cutting speed for any of these combinations. For example, in the turning of the custom-modified Haynes 263 alloy (0.02% C, 20% Cr, 2% Ti, 2% Al) using a cutting tool made of carbide M10 (94% WC, 6% Co) and various combinations of cutting tool geometry parameters, eight cutting tests were needed to obtain the relationship hs−o = f(ν) and about one hundred (dw ×f ×rn ×κr ) short-time tests for determining the optimal cutting speed corresponding to the optimal cutting temperature. The experimentally obtained correlation is, νopt =

8.25rn0.15 f 0.40 dw0.30 (sin κr )0.4

.

(4.19)

When micrograin M10 (94% WC, 6% Co) carbide was used under the same conditions, the following correlation was obtained. νopt =

8.65rn0.15 f 0.38 dw0.29 (sin κr )0.38

.

(4.20)

4.7 Influence of Workpiece Diameter The diameter of the workpiece affects the cutting process in various ways as, • The static rigidity of the machining system depends on the workpiece diameter. In boring, the diameter of the hole being bored often determines the diameter of boring bar or arbor and thus effects the static and dynamic stability of the machining system. • The workpiece diameter affects the curvature on the surface being cut, that, in turn, affects the stressed-deformed state of the layer being removed. As a result, the final inclination angle and the total length of the surface of the maximum combined stress (often referred to as the shear angle and the length of the shear plane) change with the workpiece diameter. • When the cutting speed is kept invariable, the rotational speed (r.p.m.) changes with the workpiece diameter that affects the dynamics of the process. • As discussed in Chapter 2, the interaction of the thermal and deformation waves takes place in metal cutting. As such, if the cutting speed and feed are kept invariable, the time of one turn of the workpiece changes with its diameter that greatly affects the discussed interactions. In other words, less residual thermal energy left by the previous tool pass is available at the current pass when the diameter of the workpiece increases. In practical testing, it is important to separate the influence of each factor. As cutting tests are conducted with different workpiece diameters, the workpiece diameter (Dw ) 4 invariable and its length (Lw ) should be selected accordingly to keep the ratio L3w /Dw to exclude the influence of the workpiece diameter on the system rigidity.

Cutting Tool Wear, Tool Life and Cutting Tool Physical Resource

249

Cutting tests were carried out where two diameters of the workpiece, 15 and 29 mm, were used. At first, the length of the workpiece was selected to keep the same rigidity (51×103 N/mm), then the invariable workpiece diameter was used while the length (and thus rigidity) of the workpiece was varied. The test results are shown in Fig. 4.18(a). As shown, when the rigidity is kept invariable (by corresponding reduction in Lw ), decreasing the workpiece diameters leads to a certain reduction in the tool wear rate as well in the roughness of the machined surface. However, if under the same conditions, Lw is not changed, the tool wear rate and surface roughness increase significantly. Calculations show that the total length of the surface of the maximum combined stress (often referred to as the shear angle and the length of the shear plane) insignificantly depends on the workpiece diameter. For example, changing this diameter from 10 to 500 mm leads to a 5–7% increase in the total length of the surface of the maximum combined stress (shear plane) depending upon the rake angle and uncut chip thickness.

q(°C) 900 hs qopt (µm/103 sm2)

700

x 40m/min

500

70m/min

6

3

3.0 2.5

1

2.0 120m/min

4 2

1.5 2

Rz (µm)

120m/min

Pz (N)

40m/min

55

12

3 1

8

n=70m/min

50 4

2

0 0

20

60

40

(a)

80

45 n (m/min) 0

40

80

Dw (mm)

(b)

Fig. 4.18. Influence of cutting speed and diameter of the workpiece in turning: (a) on the cutting temperature, tool wear rate and roughness of the machined surface. Work material – custommodified Haynes 263 alloy (0.02% C, 20% Cr, 2% Ti, 2% Al), tool material – micrograin carbide M10 (94% WC, 6% Co), depth of cut dw = 0.25 mm, cutting feed f = 0.09 mm/rev: 1 − Dw = 29 mm, Lw = 230 mm, 2 − Dw = 16 mm, Lw = 95 mm, 3 − Dw = 15 mm, Lw = 230 mm Z (b) on CCR and cutting force. Work material – Haynes 263 alloy (29% Cr, 2.5% Ti), tool material – carbide M20 (92% WC, 8% Co), depth of cut dw = 0.25 mm, cutting feed f = 0.09 mm/rev.

250

Tribology of Metal Cutting

On this basis, one should expect some redaction in the chip compression ratio when the diameter of the workpiece decreases. The test results, however, do not support this hypothesis. As shown in Fig. 4.18(b), with decreasing diameter, a certain increase of the chip compression ratio is the case. This is explained by the reduction in the energy required for the fracture of the layer being removed due to the increased amount of residual thermal energy (higher temperature) from the previous tool pass (see Chapter 2). It was proved by using the water-based (great cooling ability) cutting fluid for the same test conditions. When such a fluid was used, the chip compression ratio increases with decreasing workpiece diameter although such a reduction is poorly correlated with the test conditions. This is due to the variations in the interaction of the thermal and deformation waves, which also depends on the workpiece diameter (Chapter 2). The influence of the workpiece diameter shows up through the cutting temperature. When cutting with low cutting speeds (ν = 30 m/min), increasing the workpiece diameter lowers the cutting temperature bringing it down with respect to the optimal cutting temperature, the ratio of the contact stresses and tool wear rate increases, as shown in Fig. 4.19. When cutting with high cutting speeds (ν = 50 m/min), increasing the workpiece diameter reduces the cutting temperature bringing it closer to the optimal cutting temperature so that the contact stress ratio and tool wear rate are reduced. When cutting with moderate cutting speeds (ν = 40 m/min), increasing the workpiece diameter first leads to decreasing the tool wear rate and contact stress ratio when the cutting temperature reduces to the optimal cutting temperature. When the cutting temperature lowers below the optimal cutting temperature, however, increasing the workpiece diameter leads to increasing the tool wear rate and contact stress ratio. The influence of the workpiece diameter at the optimal cutting speed can be expressed by the following empirical relation, x

νopt = Cν−o Dwν−o .

(4.21)

Table 4.7 presents the value of Cν−o and xν−o for some work conditions and materials. The diameter of the hole being machined affects the cutting process significantly in boring operations. The smaller the diameter of the hole being machined (when the cutting speed is kept invariable), the greater the chip compression ratio and thus the work of plastic deformation. As a result, the cutting temperature increases. The influence of the diameter of the hole being machined in boring was studied experimentally. In the boring tests, stainless steel AISI 303 was used as the workpiece material, the diameters of the bored holes were 17, 26 and 37 mm. Cutting regime: depth of cut dw = 0.30 mm, cutting feed f = 0.06 mm/rev, ν = 40–160 m/mm, maximum radial tool wear rate hr = 50 µm. Figure 4.20 shows the influence of the cutting speed on the electromotive force (e.m.f.), chip compression ratio and tool wear rate in boring. As shown, the optimal tool wear rate depends on the diameter of the hole being machined (when the optimal cutting temperature is kept invariable). As such, with increasing hole diameter, the optimal

Cutting Tool Wear, Tool Life and Cutting Tool Physical Resource θ(°C)

251

n = 50 m/min

800 n = 40 m/min

θopt

700 n = 30 m/min

600

sc tc

n = 50 m/min

1.0 n = 30 m/min

hs (µm/103 sm2)

0.8 0.6

n = 40 m/min

0.4 n = 50 m/min

300 n = 30 m/min

n = 40 m/min

100 0

40

80 dw (mm)

Fig. 4.19. Influence of cutting speed and diameter of the workpiece on the cutting temperature, contact stress ratio at the tool–workpiece interface and optimal tool wear rate in turning. Work material – Haynes 263 alloy (29% Cr, 2.5% Ti), tool material – micrograin carbide M10 (94% WC, 6% Co) depth of cut dw = 0.25 mm and cutting feed f = 0.09 mm/rev.

cutting speed increases and the tool wear rate and the chip compression ratio decrease. Figure 4.21 further exemplifies these conclusions. In boring of holes using cutting tools made of carbide M10 (92% WC, 8% Co) when work material is stainless steel AISI 303, at the above-indicated cutting regime, the optimal Table 4.7. Values of Cν−o and xν−o in Eq. (4.21) for the depth of cut dw = 0.25 mm and feed f = 0.09 mm/rev. Materials Workpiece

Diameter of Cν−o workpiece

xν−o

Tool

Steel AISI 1045 P20 (15% TiC, 6% Co, 79% WC) Custom-modified Haynes 263 Micrograin carbide M10 alloy (0.02% C, 20% Cr, (94% WC, 6% Co) 2% Ti, 2% Al) Haynes 263 alloy (29% Cr, Micrograin carbide M10 2.5% Ti) (94% WC, 6% Co)

35–130 20–50

141 0.125 20.4 0.200

22–90

17.9 0.175

252

Tribology of Metal Cutting e.m.f.(mV) 26 mm 17 mm

e.m.f.opt

9

dw =37 mm

7

5

x

3

4

3 hs (µm/103 sm2)

2

60

40 20 0

40

80

120

160

n (m/min)

Fig. 4.20. Influence of cutting speed and diameter of the hole being machined on the electromotive force (e.m.f.) and tool wear rate. Work material – stainless steel AISI 303, tool material – carbide M20 (92% WC, 8% Co), depth of cut dw = 0.30 mm and cutting feed f = 0.06 mm/rev.

cutting speed and optimal tool wear rate correlated with the hole diameter (Dw ) as 0.52 (m/min) νopt = 16.6Dw

48.8 hs−opt = 0.22 µm/103 · sm2 Dw

(4.22) (4.23)

Using these equations, one can calculate the optimal cutting speed and optimal tool wear rate for a wide range of diameters of the machined hole. When the diameter of the machined hole increases and the cutting temperature is kept invariant and equal to the optimal cutting temperature, the chip compression ratio, ζ increases. Under this condition, it can be calculated as: ζ=

9 . 0.4 Dw

(4.24)

Cutting Tool Wear, Tool Life and Cutting Tool Physical Resource

z

253

n hs (µm/103 sm2) (m/min) nopt hv

2.8

90

28

z 2.0

70

24 hs−o

1.2

50

20 15

20

25

30

35

Dw (mm)

Fig. 4.21. Influence of diameter of the hole being machined on hs−o , νopt and ζ at the invariable optimal cutting temperature. Turning, work material – stainless steel AISI 303, tool material – carbide M20 (92% WC, 8% Co).

When the optimal cutting temperature is kept invariable, the dimension wear rate correlates with the hole diameter as: 0.30 νh = 0.486Dw

(µm/min) ,

(4.25)

(min) ,

(4.26)

The total tool life is, T =

2.06hr 0.30 Dw

and the dimension tool life is 0.22 TD = 205hr Dw



sm2 .

(4.27)

With the increase in diameter of the hole being machined (when θopt = constant), the total tool life decreases (the dimension wear rate increases) while the dimension tool life increases. This apparent contradiction is readily explained by the fact that if θopt = constant, boring of holes of greater diameters requires higher cutting speeds to achieve the same cutting temperature so that the tool would machine a greater area. When boring with low cutting speeds (ν = 72 m/min), increasing the workpiece diameter leads to a significant increase in the tool wear rate. This happens because the cutting temperature at ν = 72 m/min for diameter Dw = 37 mm is below the optimal cutting temperature. When boring with a moderate cutting speed (ν = 90 m/min), increasing the diameter of the hole being machined in boring first leads to decreasing the tool

254

Tribology of Metal Cutting

wear rate as the cutting temperature lowers and approaches the optimal cutting temperature, then, reaching its minimum at the optimal cutting temperature, the tool wear rate increases as the cutting temperature becomes lower than the optimal cutting temperature. When machining with a high cutting speed (ν = 110 m/min), the tool wear rate reduces monotonely with increasing hole diameter. This is because the cutting temperature is high, so increasing the hole diameter leads to its reduction hence it becomes closer to the optimal cutting temperature. The foregoing analysis shows that in boring, the established optimal cutting speed for a certain hole diameter cannot be used if the diameter of the hole being machined is changed. For example, if a hole of 37 mm diameter is bored at the cutting speed 72 m/min (which is optimal for a hole of 17 mm dia.), then the dimension tool life reduces by 2.36 times and the productivity of machining by 1.5 times compared to those obtained at the cutting speed 105 m/min, which is the optimal cutting speed for the latter hole diameter. Unfortunately, the influence of the hole diameter has never been considered as a factor in boring operations.

4.8 Plastic Lowering of the Cutting Edge 4.8.1 Description As discussed in Chapter 3, highest tool temperatures occur at the tool–chip interface. When the rake face is heated to temperatures 900–1200◦ C, a plastic flow begins in volumes adjacent to this face. This flow takes place due to adhesion bonding between the rake face and the chip. In the case of carbide tool materials, plastic deformation is greater in the cobalt matrix. This plastic deformation results in tearing-off of carbide (WC and TiC) grains from “soft” cobalt layers (matrix) that undergo severe plastic deformation, “ploughting” this “soft” layer by inclusions contacting in the work material, and “spreading” of the tool material on the chip and workpiece contact surfaces. If the temperature increases even further, a liquid layer forms between tool and workpiece due to diffusion leading to the formation of low-melting-point compound Fe2 W having a melting temperature Tm = 1130◦ C. This layer is quickly removed in cutting [14]. At high cutting speeds, particularly in the machining of difficult-to-machine work materials, in parallel with plastic flow and spreading of the tool material over the chip and tool contact surfaces (that was conclusively proven by special tests with radioactive isotopes[14]), the plastic lowering of the cutting edge takes place. This plastic lowering is observed not only carbide with, but also when PCD, metaloceramic and ceramic tool materials are used. Often, in the machining of difficult-to-machine materials and in high speed machining, the plastic lowering of the cutting edge is the predominant cause of premature tool failure. Typical appearance of the discussed plastic lowering is shown in Fig. 4.22. Plastic lowering is the plastic deformation of the cutting wedge (a part of the tool between the rake and the flank contact surfaces) in a way, as shown in Fig. 4.23(a). As shown, the rake (γ) and flank (α) angles change due to plastic lowering hγ of the cutting edge.

Cutting Tool Wear, Tool Life and Cutting Tool Physical Resource

(a)

255

(b)

Fig. 4.22. Typical appearance of the plastic lowering of the cutting edge: (a) on a carbide insert and (b) on a PCD insert.

Strain

ep

Workpiece

f

eo

Tool

Time

lγ hg

g

(b)

q (°C) 1800

hf

1400 1200

5 4 3

1000 800

ha

la a

2

(a)

600 500

1

400 200

300

400 500

800

1000

2000 t (MPa)

(c) Fig. 4.23. Plastic lowering of the cutting edge: (a) parameters, (b) a typical engineering creep curve, (c) creep diagram for typical components of carbide: 1 – Co, 2 – WC–Co, 3 – WC–TiC–Co, 4 – WC and 5 – TiC.

This lowering is characterized by four parameters lγ , lα , hγ and hα . When these parameters reach a certain limit, the breakage of the cutting wedge takes place. To prevent this from happening, the transition surface between the rake and the flank surface (often referred to in machining practice as the hone) are often made as fillet or chamfer instead of the sharp cutting edge (often referred to as the cutting edge preparation).

256

Tribology of Metal Cutting

4.8.2 Cause As conclusively proven by Makarow [14] and Talantov [24], the primary cause of the plastic lowering of the cutting wedge is high-temperature creep. It is known that when temperatures at the tool–chip interface reach 1000–1200◦ C, the cutting wedge deforms plastically. Creep is the progressive deformation of a material at constant stress. A typical engineering creep curve shown in Fig. 4.23(b) represents the dependence of plastic deformation of a metal when constant load and temperature are applied. As shown, upon loading of a preheated specimen, deformation increases rapidly from zero to a certain value ε0 known as the initial rapid elongation [19]. There is no need for additional energy for this deformation because it occurs due to the thermal energy that already exists in the specimen, so the work done by the internal forces begins with the level of energy that has already been achieved. In other words, if the temperature is a characteristic of the thermal energy, and deformation and stress characterize the work done by the external forces, then the critical amount of energy accumulates in the material as the result of their summation. Among the phases normally present in carbides used as the tool material, the plastic deformation is greater in the cobalt phase, as shown in Fig. 4.23(c), which generalizes the experimental results obtained by Makarow [14]. The lines in this diagram separate low and high temperature creep. At low temperature, plastic deformation does not exceed 1% however it reaches 300% on the whole, without fracture (due to diffusion phenomena) at high temperature creep. The separation between low and high temperature creep is rather conditional because the occurrence of various creep mechanisms [19] depends not only on temperature but also on the stressed state and the level of stresses. Plastic lowering of the cutting edge can be
characterized by the ratio of radial wear, hr and with the flank land, hf , i.e. hpl = hr hf . When there is no plastic lowering, hpl is determined by the tool geometry and does not depend on the machining regime. Experimental observations of changing hr and hf over tool life period showed that hpl does not remain invariable. Its variation and particular value are affected by the properties of the work and tool materials, machining regime, cutting fluid, etc. For example, increasing the cutting feed leads to the reduction of hpl (Fig. 4.24(a)) that is attributed to increasing the contact stresses and temperatures. As shown in Fig. 4.24(b), the values of hpl are reduced with the increase in cutting feed when the cutting temperature is equal to the optimal cutting temperature and kept unchanged. The main difficulty in the determination of the topography of the plastic lowering is that it takes place simultaneously with the wear of the tool flank. To resolve the problem, Talantov [24] proposed to present the experimental results on plastic lowering using different scales for hr and lγ shown in Fig. 4.25(a). The example of the results is shown in Fig. 4.25(b). As shown, the developments of hf , hγ and hα in time follow the shape of the engineering creep curve shown in Fig 4.23(b). As known [19], high-temperature creep is the process of plastic deformation where two opposite-signed and equally intensive processes take place namely the growth of stresses (causes plastic deformation) and their relaxation (caused by plastic deformation).

Cutting Tool Wear, Tool Life and Cutting Tool Physical Resource hpl hs (µm/103 sm2)

q (°)

257

hpl

q 0.09

3

0.07

900

dw =0.50 mm dw =1.00 mm

0.07

2

800

0.05

700

0.03

hpl hs 0.05

1

dw =2.00 mm

0.03

0.2

0.3

0.4

0.01 0.1

600 f (mm/rev)

0 0.5

0.3 f (mm/rev)

0.2

Fig. 4.24. Influence of cutting feed in turning stainless steel AISI 303: (a) on cutting temperature, tool wear rate and hpl criterion, tool material – carbide M20 (92% WC, 8% Co), ν = 72 m/min, dw = 5 mm, γ = 15◦ , α = α1 = 10◦ , κr = 45◦ , κr1 = 10◦ , rn = 1 mm, (b) on hpl criterion under the optimal cutting temperature θopt = 850◦ C, tool material – carbide P10 (14% TiC, 8% Co), γ = 10◦ , α = α1 = 10◦ , κr = 45◦ , κr1 = 10◦ , rn = 1 mm.

Ig t = 0s t = 10s t = 30s t = 60s

hg

ha, hg (µm)

hf (µm) Tool breakage

40

80

hf

30

60

20

40 hg

10

20

ha 0

(a)

2

0 4

6

8

10

t (min)

(b)

Fig. 4.25. Plastic lowering of the cutting edge. Turning, work material – steel AISI 1045, tool material – carbide P20 (77% WC, 15% TiC, 8% Co), ν = 180 m/min, dw = 2 mm, f = 0.3 mm/rev: (a) dynamics of the lowering and (b) perimeters of lowering as functions of time.

As explained [16], the stress relaxation has temperature-diffusion nature. Therefore, it is reasonable to assume that plastic deformation in high-temperature creep takes place along the isotherms of a quasi-state temperature field. Talantov presented another experimental evidence to support the suggestion that the plastic lowering of the cutting edge is related to high-temperature creep [24]. He constructed

258

Tribology of Metal Cutting lc = 1.10mm

lc = 1.95mm

l1 = 0.50mm

l1 = 0.77mm 325

655 640

525 460

300

410°C

575

530

615°C

485°C

(a)

610

585 405 430 300°C

(b)

Fig. 4.26. Temperature field in the cutting wedge in turning. Work material – steel AISI 1045, ν = 1 m/s, f = 0.3 mm/rev, dw = 2 mm, for two groups of tool materials: (a) carbide M20 (92% WC, 8% Co and (b) carbide P20 (77% WC, 15% TiC, 8% Co).

temperature fields for two basic groups of carbide tool materials experimentally as shown in Figs. 4.26(a) and (b). The length of the plastic part lc−p of the tool–chip contact length lc was measured for each tool and new tools were made with the restricted rake face equal to lc−p . The experimental comparison of the plastic lowering of the cutting edge of the tool with the natural and restricted contact lengths showed that this lowering is much smaller for the latter tools. This is because much less heat is generated due to the friction at the tool–chip interface so that a smaller thermal energy enters the tool. By excluding this elastic part, the amount of the thermal energy entered into the cutting tool substantially reduces the plastic lowering of the cutting edge. This explains the major advantages of the tool with the restricted contact length known in practice. It is also known [19,24] that significant intensification of high-temperature creep takes place if the amplitude of cyclic load increases. As discussed in Chapter 1, the amplitude of the cyclic cutting force grows when seizure occurs at the tool–chip interface (Fig. 1.25) that results in the saw-toothed continuous fragmentary chip (Figs. 1.30–1.33). Therefore, a noticeable increase in the plastic lowering of the cutting edge should be observed under this condition. Figure 4.27 shows parameters characterizing the plastic lowering of the cutting edge under the high-amplitude cutting force during the formation of this chip type. Significant intensification of the plastic lowering of the cutting edge in this case is readily observed if one compares Figs. 4.27 and 4.25(b). It explains the well-known fact: tool life reduces significantly when the conditions at the tool–chip interface result in the occurrence of the saw-toothed continuous fragmentary chip. A comparison of the model of plastic lowering (shown in Figs. 4.23(a) and 4.25(a)) and the data shown in Fig. 4.27 shows that the model of plastic lowering is more complicated than described so far. As shown, for example, hα first increases with increasing

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259

ha, hg, hf (µm)

160

hf

120

80

hg 40

ha 0

2

4

6

8

10

t (min)

Fig. 4.27. Intensification of the parameters of the plastic lowering of the cutting edge under the condition of the increased cyclic loading (seizure). Turning of modified AK Steel (AISI Austenitic Stainless Steel 305), ν = 1 m/s, f = 0.3 mm/rev, dw = 2 mm and carbide M20 (92% WC, 8% Co).

hγ and then, reaching a certain value, does not change any further. Talantov [24] suggested that this is because the so-called wear land (of width hf in Fig. 4.23(a)) increases not only due to the regular wear of the tool flank but also due to bulk deformation of the cutting wedge. To verify this suggestion, a special turning cutting test was carried out where the actual width hf −a of the wear land was measured and the calculated wear land hf −c as determined through the radial tool wear hr and normal flank angle is, hf −c = hr /tan αn .

(4.28)

The following machining regime was used: workpiece material – AISI steel 1045, cutting feed, f = 0.3 mm/rev, depth of cut dw = 2 mm; cutting tool: tool materials – carbide M20 (92% WC, 8% Co) and carbide P20 (77% WC, 15% TiC, 8% Co), tool geometry: rake angle γn = 0◦ , flank angles α of the major and minor cutting edges αn = α1n = 10◦ , tool cutting edge angle of the major cutting edge κ = 45◦ , tool cutting edge angle of the minor cutting edge κ1 = 15◦ , tool nose radius rn = 0.25 mm. The test results shown in Fig. 4.28 fully support the Talantov’s suggestion. As shown, the actual width of the wear land hf −a is greater than the calculated (Eq. (4.28)) width of this land, hf −c . This is because the actual width of the wear land increases not only due to tool wear but also due to the creep of the cutting wedge. Analysis of the temperature field shown in Fig. 4.26(a) and the contact conditions at the tool–chip interface (discussed in Chapter 3) allows offering the following explanations to the described phenomena. The cutting wedge is subjected to complicated plastic deformation in the cutting process. A model of this deformation is shown in Fig. 4.29. A part of the cutting wedge (Zone 2 in Fig. 4.29) deformed and moved toward the tool flank more intensively than its other parts

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hf−a, hf−m(mm) 1045-M20 n =1.67m/s

hf−a 0.09

hf−m

1045-M20 n=1.33m/s

hf−a 0.06

hf−m

1045-P20 n =1.67m/s

hf−a 0.03

hf−m 4

0

8

12

t (min)

Fig. 4.28. Comparison of the actual (experimentally obtained), hf −a and calculated, hf −c widths of the wear land.

hg Zone 1

Zone 2

Zone 3

K

O hf−a

ha

Fig. 4.29. A model of the plastic lowering of the cutting edge.

shown as Zones 1 and 2. Such a behavior is explained by the temperature-deformation stress relaxation where the temperature is a decisive factor. Starting with a certain temperature, the intensity of stress relaxation increases significantly. The process of plastic deformation where the intensity of stress growth is equal to that of stress relaxation due to plastic deformation relates to creep. Analysis of the temperature fields of the cutting edge (for example shown in Fig. 4.26) shows that there are some zones heated to significant temperature over the whole volume from the rake face to the tool flank, as shown by the corresponding isotherms. High-temperature creep takes place along these isotherms that leads to the pushing out of some volumes of the tool material below the formed wear

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261

land on the tool flank. As tool wears, high-temperature creep of the material in Zone 2 becomes a continuous process as the temperatures in this zone increase proportionally to tool wear. At the same time, any motion of the tool material within Zone 1 is impossible as this zone is loaded by the compressive stresses from the rake and flank contact surfaces. Moreover, the temperatures in Zone 1 are lower than those in Zone 2. As a result, the tool material in Zone 1 is not subjected to creep. As for Zone 3, high-temperature creep does not occur here because of a number of reasons: lower temperatures, greater crosssectional areas and much lower contact stresses. As such, these temperatures in Zone 3 cause stress relaxation in this zone without its plastic deformation. The description above allows us to conclude that some zones in the cutting wedge can be subjected to plastic deformation under certain combination contact stresses/temperatures. As such, this plastic deformation causes the growth of the wear land on the tool flank without actual increase in tool wear. Therefore, the notion of the wear land on the tool flank surface is conditional as this land forms not only due to tool wear but also due to high-temperature creep (and thus plastic deformation) of the cutting wedge. This conclusion is of particular importance for cutting tools with coatings. For years Talantov [24] asked a simple question “How come a coating is able to reduce tool wear of the tool flank for a long time period? It is known that the coating thickness (the thickness of the coated layer) typically ranges from 3 to 10 µm. If the cutting wedge would be ideally rigid having the flank angle αn = 10◦ and the coating thickness is 8 µm, then this coating should be gone when the width of the flank wear land reaches 40 µm. Therefore, the coating under these conditions should be wiped out during the first minute of machining. In practice, however, such a coating reduces the tool wear rate during several dozens of minutes as the width of the flank wear land reaches 0.4–0.7 mm. The known explanations of this fact rely on the existence of “an overhung” of the coating material over the tool flank although not one study can find this overhung in reality [24]. Talantov proposed and proved a much simpler and real mechanism to explain the discussed fact. Figure 4.30 shows the cutting wedge after 10 min of cutting. As shown, the coating exists over the whole flank wear land having a width of 0.4 mm. Therefore, this is not just the wear land but rather it is the contact land formed due to the abovedescribed plastic lowering of the cutting wedge. To demonstrate the validity of such an explanation, Talantov studied [24] the formation of the contact length in cutting tools with TiN coating. Figure 4.31 shows the cutting wedge after 3 min of cutting. As shown, the coating is still intact on the tool flank contact surface (except for some random chipping) while there is no coating on the rake face in the zone, where certain volumes of the tool material were pushed out towards the tool flank. According to Talantov [24], the mechanism of high-temperature creep (the model shown in Fig. 4.29) can be described as follows. In Zone 2 (Fig. 4.29), the fist phase of the carbide tool material to deform is the cobalt matrix. Due to the action of the contact stresses, this phase deforms along the direction shown by arrows in Fig. 4.29. This leads to the destruction of the cobalt matrix which holds carbide particles as a frame. To prove

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Tribology of Metal Cutting

Fig. 4.30. Micrograph of the cutting wedge. Cutting conditions: work material – steel AISI 1070, tool material – M10, coating – TiN, cutting speed ν = 90 m/min, feed f = 0.1 mm/rev, depth of cut dw = 1.5 mm, cutting time τ = 10 min, magnification ×120.

Fig. 4.31. Micrograph of the cutting wedge. Cutting conditions: work material – steel AISI 1070, tool material – P20, coating TiC, cutting speed ν = 100 m/min, feed f = 0.3 mm/rev, depth of cut dw = 1.5 mm, cutting time τ = 3 min, magnification ×100.

Cutting Tool Wear, Tool Life and Cutting Tool Physical Resource

263

that this is the case, the worn tool wedge was mounted, polished and etched in a ferric chloride solution in hydrochloric acid. The results of the described destruction can be shown as a black region in Fig 4.31. As shown, the configuration of this black region resembles the model shown in Fig. 4.29. The destruction of the cobalt matrix as a frame can clearly be shown by comparing the initial carbide structure shown in Fig. 4.32(a) and that after 7 min of machining shown in Fig. 4.32(b). This explains the fractography of the broken cutting wedge shown in Fig. 4.33. As shown, the surface of fracture includes two distinctive zones: one closer to the rake face represents the black region shown in Fig 4.31 while the other resembles the fractography of normal brittle fracture of tool carbide. To evaluate the described destruction quantitatively, a microhardness scanning test was carried out along the lines shown in Fig. 4.34(a). Figure 4.34(b) shows the distribution of microhardness along these lines. As shown, the maximum microhardness was observed in the regions of the cutting wedge adjacent to Zone 1 as this zone is always subjected

Fig. 4.32. Micrographs of the cutting wedge in Zone 2: (a) new tool and (b) tool after 7 min of machining. Work material – tool steel HVG (1% C, 1% Cr, 1.5% W, 1% Mn), tool material M30 (82% WC, 7% TaC, 3% TiC, 8% Co), cutting regime: cutting speed ν = 3.3 m/s, feed f = 0.3 mm/rev, depth of cut dw = 1.5 mm, cutting time τ = 7 min, magnification ×2000.

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Tribology of Metal Cutting

Fig. 4.33. Cutting wedge breakage as a result of plastic lowering. Fractography of breakage shows two distinctive surfaces of fracture.

to high contact compressive stresses during machining [25,26]. The normal, for the tool material used in the test, microhardness was observed in the regions of the cutting wedge adjacent to Zone 3 as these regions were not subjected to high temperature and stresses in cutting. The lowest microhardness readings are observed in the regions of the cutting wedge adjacent to Zone 2 as a result of high temperature enhanced difussional stress relaxation that led to the softening of the tool material in these regions.

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265

HV (MPa)

18000

I II

17000 16000

III 15000 14000 13000 0

0.2

0.4

(a)

0.6

0.8

1.0

Distance from the flank (mm)

(b)

Fig. 4.34. Cutting wedge structure after 7 min of machining: (a) micrograph ×400, (b) microhardness distribution along lines I, II and III. The cutting conditions are the same as in Fig. 4.31.

hf

hf

hg

Talantov suggested [24] that the plastic lowering of the cutting edge takes place differently for different tool materials. He developed two distinctive modes shown in Figs. 4.35 (a) and (b) for carbide tool. The first one shown in Fig. 4.35(a) is characterized by the plastic lowering of the cutting and by bulging of the tool flank surface. This mode is common for carbides having low thermal conductivity as carbides of ISO P group (especially containing titanium carbides) when they are used for the machining of difficult-to-machine work materials of high strength and low thermoconductivity

ha

(a)

ha

(b)

Fig. 4.35. Two modes of plastic lowering of the cutting edge: (a) for low-thermoconductivity carbides, ISO P group (b) for high-thermoconductivity carbides, ISO M group.

266

Tribology of Metal Cutting

i.e. when high temperature and high stress region in the cutting wedge are located close to the cutting edge. The second mode shown in Fig. 4.35(b) is particularly for carbides of higher thermoconductivity such as carbides of ISO M group, especially when the uncut chip thickness (and thus the contact length) is great. Tool breakage takes place when plastic lowering of the cutting edge reaches a certain limit. This is because great interfacial stresses develop between plastically deformed due to creep volumes of the tool material in Zone 2 and those in Zones 1 and 3. As a result of these stresses, fracture takes place over the border between Zones 1 and 2 (more common) or between 2 and 3 (less common). The former case is shown in Fig. 4.33. Reading the described model, one may wonder if the plastic lowering of the cutting edge is not a continuous phenomenon but rather occurs during a short time just before the actual breakage of the cutting wedge. In other words, it can be assumed that the occurrence of the plastic lowering of the cutting edge results in a significant increase in the cutting force that, in turn, leads to breakage. To prove that this is not the case, a special cutting test was carried out where the components of the cutting force were recorded using a high sensitive tool dynamometer as well as the level of micro vibrations of the cutting tool using built-in accelerometers. The results of this test indicated that there is no increase in the cutting force and tool vibration or any other spikes prior breakage of the cutting wedge. Moreover, a good repitition of tool breakage life (12 min 30 s ±12 s) confirms that the plastic lowering of the cutting edge is a steady-state physical process.

4.8.3 Reduction Plastic lowering of the cutting edge can be controlled to a large extent by the parameters of the tool geometry. Among these parameters, the flank angle, the configuration of the rake surface and the nose radius are of prime importance. Figure 4.36 shows profiles of the flank surface for different flank angles. As shown, the smaller the flank angle, smaller is the plastic lowering of the cutting edge. This leads to an important conclusion known from machining practice: in machining of difficult-to-machine materials, the flank angle should be chosen as small as is possible. The limitation is the possible interference of the tool flank face and the machined (transient) surface. Therefore, an additional module should be included in commercial programs for the verification tool path on CNC machines that can verify the absence of the said interference. Figure 4.37 shows the influence of the configuration of the rake surface. As shown, the maximum cutting edge lowering occurs when “normal configuration” of the tool rake face is used. A significant reduction in this plastic lowering is achieved when the rake face is reinforced by a chamfer. It follows from Fig. 4.37 that the optimal geometry of this chamfer exists for a given cutting condition. It should be pointed out that the width of the discussed chamfer is much lower than the uncut chip thickness hence the tool is not of the so-called negative geometry. Figure 4.38 shows the influence of the tool nose radius. As shown, with the increase in nose radius, plastic lowering decreases particularly in the region of the tool point.

Cutting Tool Wear, Tool Life and Cutting Tool Physical Resource

267

(mm) 80

60

40

20

a = 5° 0

10°

15°

30

a = 25°

20°

60

90

120

150

(mm)

Fig. 4.36. Shapes of the tool flank surface for different flank angles. Turning, work material – steel AISI 1045, tool material M10 (92% WC, 8% Co), Cutting regime: cutting speed ν = 2.4 m/s, feed f = 0.4 mm/rev, depth of cut dw = 2 mm. Magnification along the vertical axis × 40, along the horizontal axis ×1000.

(µm) 750 500 250 0

hα 1

1

10 20 30

2

3

(µm)

1

fg = 0.18 g = +10°

gf = −5°

2

3

fg = 0.18 g = +10°

gf = −10°

g = +10°

Fig. 4.37. Shapes of the tool flank surface for different configurations of the rake surface. Curve 1 – cutting time τ = 10 s, 2 – τ = 30 s, 3 – τ = 60 s. Turning, work material – steel AISI 1045, tool material P20 (79% WC, 15% TiC, 6% Co), cutting regime: cutting speed ν = 3.3 m/s, feed f = 0.4 mm/rev and depth of cut dw = 2 mm.

268

Tribology of Metal Cutting (mm)

rn = 0

90

60

rn = 0.5 mm 30

0

30

40

50

60

(mm)

Fig. 4.38. Plastic lowering of the tool point. Turning, work material – steel AISI 1045, tool material P20 (79% WC, 15% TiC, 6% Co), Cutting regime: cutting speed ν = 3.3 m/s, feed f = 0.4 mm/rev, depth of cut dw = 2 mm. Magnification along the vertical axis ×40, along the horizontal axis ×1000.

This is an important conclusion since this point forms the diameter of the part being machined. The influence of the tool material on plastic lowering of the cutting edge can be summarized as follows: • The intensity of plastic lowering reduces when the cobalt matrix of a carbide tool material is made harder by alloying it with tungsten. The smaller the percentage of carbon in carbide, the higher the solubility of tungsten in cobalt, and lower the plastic lowering. • The intensity of plastic lowering increases with the decrease in the thermoconductivity of the tool material. It can be attributed to the changes in the tool–chip contact length (discussed in Chapter 3) and to the shift of the regions of higher temperature of the cutting wedge closer to the cutting edge. • The intensity of plastic lowering in carbide tool materials increases with higher cobalt content. • The intensity of plastic lowering increases with the increase in the size of carbide grains that relates to increasing the cobalt spacing between grains and reduction of thermoconductivity. When plastic lowering occurs, it changes the rake and flank cutting tool angles that leads to further increase in the tool wear rate. Chipping and then breakage of the cutting wedge occur at the final stage of creep. To slow down high temperature creep,

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269

the cutting edge, when it is possible, should be ground with radius or a small chamfer (land) and a zero flank angle should be ground on the tool flank surface, the flank angle should be as small as possible. Cutting edge preparation, including honing the rake and flank surface adjacent to the cutting edge, is proven to be very useful in machining difficult-to-machine materials. Proper edge geometry affects tool performance in two specific ways. First, it heavily influences tool reliability. Properly honed tools can improve the repeatability of machining operations. Second, proper edge preparations improve tool life by reducing the common causes of failure, such as chipping and heat-induced failures. Tool end users can realize dramatic cost reductions and productivity improvements by applying state-of-the-art edge preparation to cutting tools, whether the tools are a manufacturer’s generic line or an end-user’s specific tooling. The return on investment for proper edge preparation services is quite high for both new and reground cutting tools.

4.9 Resource of the Cutting Wedge As discussed in Chapter 2, the energy flows to the zone of the fracture of the layer being removed through the cutting wedge (defined as a part of the tool located between the rake and the flank contact areas). Out of three components of the cutting system, namely, the cutting tool, the chip and the workpiece, the only component that has an invariable mass of material and which is continuously loaded during the cutting process, is the cutting wedge. As such, the overall amount of energy, which can be transmitted through this wedge before it fails, is entirely determined by the physical and mechanical properties of the tool material. On the contrary, the material of the chip is not subjected to the same external force because the chip is an ever growing component, i.e. a new section is added to the chip during each cycle of chip formation while “old” sections move out of the tool–chip interface and thus do not experience the external load. The same can be said about the workpiece whose volume and thus mass changes during the cutting process as well as the area of load application imposed by the cutting tool. When the cutting wedge loses its cutting ability due to wear or plastic lowering of the cutting edge (creep), the work done by the external forces that causes such a failure is regarded as the critical work. As was established by Huq and Celis, a direct correlation exists between wear and the dissipated energy in sliding contacts [27], so for a given cutting wedge, this work (or energy) is a constant value. The resource of the cutting wedge, therefore, can be represented by this critical work. According to the principle of physical theory of reliability [19], each component of a system initially has its resource and this resource is spent during operation time at a certain rate depending on the operating conditions. This principle is valid for a wide variety of operating conditions, provided changes from one operating regime to another do not lead to any structural changes in material properties (reaching the critical temperatures, limiting loads, chemical transformations, etc.). As such, the resource of a cutting tool, rct can be considered as a constant, which does not depend on a particular

270

Tribology of Metal Cutting

way of its consumption, i.e. τ1 τ2 rct = f (τ, R1 )dτ = f (τ, R2 )dτ, 0

(4.29)

0

where τ1 and τ2 are the total operating times on the operating regime R1 and R2 , respectively, till the resource of the cutting tool is exhausted. The initial resource of the cutting tool can be represented by the above discussed critical energy and the flow of energy through the cutting tool exhausts this resource. The amount of energy that flows through the cutting tool depends on the energy to separate the layer being removed, which, in turn, defines the total energy Ucs required by the cutting system to exist (Chapter 2). Therefore, there should be a strong correlation between a parameter (or metric) characterizing the resource of the cutting tool (for example, flank wear VBB ) and the total energy Ucs . To demonstrate the validity of the discussed principle, a series of cutting tests (bar longitudinal turning) were carried out. The work material was steel AISI 52100: chemical composition – 0.95% C, 1.5% Cr, 0.35% Mn, 0.25% Si; tensile strength, ultimate – 689 MPa, tensile strength, yield – 558 MPA, annealed at 780◦ C to hardness 192 HB. Cutting tool material – carbide P10 (cutting inserts SNMG 12 04 08). The experimental results are shown in Table 4.8. It follows from this table that there is a very strong correlation between the total work required by the cutting system and the flank wear. This correlation does not depend on a particular cutting regime, cutting time and other parameters of the cutting process. Figure 4.39 shows the correlation curve [26]. The discovered correlation between the energy passed through the cutting wedge and its wear can be used for the prediction of tool life and optimal cutting speed allowing the avoidance of expensive and time-consuming tool life tests. Moreover, the multiple experimental results, obtained in machining of different work materials using different cutting tools, proved that this correlation holds regardless of the particular manner the resource of the tool was spent. The essence of the method can be described as follows: The energy required by the cutting system during the time period corresponding to tool life Tct can be represented as Ucs = Wcs Tct ,

(4.30)

where Wcs is power required by the cutting system (W). Note that Ucs , when selected for a given tool material using the correlation curve similar to that given in Fig. 4.39 for the accepted tool life criterion, is the sole characteristic of the tool material, i.e. its resource can be used for calculating the tool life in cutting different work materials.

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Table 4.8. Conditions of tests and experimental results. Test number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Feed (mm/rev)

Depth of cut (mm)

Operating time (s)

Flank wear (VBB ) (mm)

Energy of the cutting system (kJ)

0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.09 0.09 0.09 0.09 0.09 0.12 0.12 0.12 0.12 0.14 0.14 0.07 0.07 0.07 0.07

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.8

8540 6680 4980 1640 9120 7660 6260 4900 3450 5380 4240 3150 2075 1036 2980 1940 1190 938 1874 2840 3820 4810 775 1520 2350 3220 675 1315 1295 2610 5420 1316

0.45 0.41 0.39 0.29 0.45 0.42 0.41 0.37 0.35 0.38 0.34 0.30 0.26 0.20 0.37 0.32 0.27 0.15 0.18 0.22 0.25 0.31 0.20 0.23 0.26 0.27 0.20 0.21 0.21 0.27 0.44 0.20

0.88 0.63 0.52 0.25 0.91 0.68 0.55 0.41 0.47 0.65 0.35 0.33 0.24 0.15 0.37 0.30 0.17 0.05 0.10 0.22 0.17 0.39 0.08 0.18 0.29 0.30 0.18 0.12 0.13 0.30 0.82 0.19

VBB (mm)

0.4

0.3

0.2

0.1 0

2

4

6

8

Ucs ×10−5(J)

Fig. 4.39. Correlation curve (after Astakhov [25]).

272

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The power of the cutting system (Wcs ) is determined as a product of the power component of the cutting force (Fz ) and the cutting speed (ν), i.e. Wcs = Fz ν

(4.31)

In turn, the cutting force Fz can be determined experimentally depending upon the cutting parameters as, n

Fz = CFz dwz f mz νkz ,

(4.32)

where CPz is a constant of the work material and nz , mz and kz are the exponents. Substituting Eqs. (4.31) and (4.32) into Eq. (4.30) and expressing tool life, one can obtain an equation which determines tool life for a given cutting regime. Tct =

Ucs . n CPz dwz f mz νkz +1

(4.33)

If it is necessary to know the cutting speed corresponding to the desired tool life, then Eq. (4.33) can be expressed as,  ν=

Ucs n CPz dwz f mz Tct



1 kz +1

(4.34)

It is obvious that Ucs selected depending on the tool flank wear depends not only on the properties of the tool material but also on the tool geometry. Therefore, the correlation curve Ucs = f(VB) should be corrected accounting for the particular tool geometry. As a result, there are countless number of possible combinations “cutting-tool material-tool geometry” to account for the influence of the tool geometry. To avoid the consideration of the influence of tool geometry, the volumetric or mass tool wear (mν ) Eq. (4.2) can be used instead of VBB . The results of foregoing analysis suggest that the most prospective way to achieve repeatability of cutting tool with inserts is the certification of cutting inserts of standard shapes. The number of standard shapes of cutting inserts (including their geometry) is relatively small so that each insert producer should be able to provide a correlation curve U = f (mν ) for each shape and tool material. Table 4.9 presents some correlations for different tool materials and for different shapes of cutting inserts obtained experimentally using basic groups of the work material (low-, medium- and high-carbon steels, low and high alloys including chromium- and nickel-based, titanium alloys). It has been proven that the obtained correlation curves do not depend on the particular work material, machine or any other cutting conditions, so they are properties of the considered tool materials. The correlations in Table 4.9 were obtained for VBB ≤ 0.4 mm. The data presented in Table 4.9 are valid under the condition that the tool material does not lose its cutting

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Table 4.9. Correlation curves for some tool materials. Tool material

ISO code of the shape Correlation curve

TS332 (99% Al2 O3 + 1% MgO–2300HV) VOK60 (60% Al2 O3 , 40% TiC 94 HRA) Silinit-P (Si3 N4 + Al2 O3 , 96 HRA) TN20 (75% TiC, 15% Ni, 10% Co, 90 HRA) Kiborit (96% CBN, KNH 32–36GPa)

SNMN 120404M

Critical temperature (◦ C)

  U = exp 9.6 VB2 

1200  2

SNMN 120404M

U = exp 10.91 VB

SNMN 120404M

U = 573VB2

SNMN 120404M

U = 434.46 × 10−3 VB2 780

RNMM1200404M

U = 50 VB½

1200 1200

1400

properties due to excessive temperature. For example, the data for Silinit–P is valid if the cutting temperature does not exceed that in the cutting of steel with feed f = 0.07 mm/rev, depth of cut dw = 0.1 mm and cutting speed ν = 3.3 m/s. If the cutting speed is increased to ν = 4 m/s, this material loses its cutting ability hence the correlation curve presented in Table 4.9 is no longer valid. It has to be pointed out that the limiting work is a complex integral index of the cutting tool resource and intensity of its “spending.” This work is not the same for two geometrically alike cutting inserts made of different tool materials as their application for the same work material at the same machining regime results in different works of chip formation defined by the chip compression ratio (Chapter 2). It is explained by different contact processes at the tool–chip and tool–workpiece interfaces. As a result, tool lives for the inserts with close relationships Ucs = f(VBB ) (Fig. 4.39) but made of different tool materials may not be the same or even close. The foregoing analysis suggests that using the established correlation Ucs = f(VBB ), it is possible to choose the limiting tool wear and then using this selected value to calculate the limiting work. Using this limiting work, one can calculate tool life under a given cutting regime or the cutting speed for the desirable tool life using the following steps: Calculation of tool life • Select the maximum allowed tool wear (VB). • Using correlation formulas similar to that shown in Table 4.9, calculate the limiting work. • Conduct a short cutting test for the chosen cutting regime to determine the cutting force Pz and the maximum cutting temperature. • Calculate tool life as T = U/(Pz ν). If the accuracy of the cutting force determination is insufficient, then the cutting energy can be determined using the chip compression ratio (see Chapter 2) or direct measurements of the power of the driving motor.

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• Compare the maximum cutting temperature obtained from the test and the limiting temperature for the selected tool material to assure that the former is lower than the latter. Calculation of the cutting speed for a given tool life • Choose the critical wear (VBB ) and the desired tool life (T ). • Using correlation formulas similar to that shown in Table 4.9, calculate the limiting work. • Conduct a short cutting test establishing correlations Pz = CPz νnz and θ = f (ν).    • Calculate the cutting speed as ν = nz +1 U/ T × CPz . • Compare the maximum cutting temperature obtained from θ = f (ν) and the limiting temperature for the selected tool material to assure that the former is lower than the latter. In the author’s opinion, new reference books on cutting tool, cutting inserts and tool materials issued and published by The National Institute of Standards and Technology and by ISO should contain similar tables to help end users to make meaningful selection of the cutting tool and tool materials for specific applications.

References [1] Schey, J.A., Tribology in Metalworking, American Society for Metals, Metals Park, Ohio, 1983. [2] Olson, M., Stridh, B., Söderberg S., Sliding wear of hard materials – the importance of a fresh countermaterial surface, Wear, 124 (1988), 195–216. [3] Stephenson, D.A., Agapiou, J.S., Metal Cutting Theory and Practice, Marcel Dekker, New York, 1996. [4] Trent, E.M., Wright, P.K., Metal Cutting, Butterworth-Heinemann, Boston, 2000. [5] Childs, T.H.C., Maekawa, K., Obikawa, T., Yamane, Y., Metal Machining. Theory and Application, Arnold, London, 2000. [6] Jawahir, I.S., Van Luttervelt, C.A., Recent developments in chip control research and applications, Annals of the CIRP, 42 (1993), 659–693. [7] Loladze, T.N., Strength and Wear of Cutting Tools (in Russian), Mashgiz, Moscow, 1958. [8] Gordon, M.B., The applicability of binomial law to the process of friction in the cutting of metals, Wear, 10 (1967), 274–290. [9] Usui, E., Shirakashi, T., Mechanics of metal cutting – from “description” to “predictive” theory. In On the Art of Cutting Metals – 75 Years Later, Vol. 7, Production Engineering Division (PED), ASME, Phoenix, USA, 1982, pp. 13–15.

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[10] Luttervelt, C.A., Childs, T.H.C., Jawahir, I.S., Klocke, F., Venuvinod, P.K., Present situation and future trends in modelling of machining operations. Progress report of the CIRP Working Group “Modelling of Machining Operations,” Annals of the CIRP, 74 (1998), 587–626. [11] Shuster, L.S.H., Adhesion Processes at the Tool-Work Material Interface (in Russian), Moscow, Machinostroenie, 1988. [12] Marinov, V., Experimental study on the abrasive wear in metal cutting, Wear, 197 (1996), 242–247. [13] Taylor, F.W., On the art of cutting metals, Transactions of ASME, 28 (1907), 70-350. [14] Makarow, A.D., Optimization of Cutting Processes (in Russian), Machinostroenie, Moscow, 1976. [15] Granovsky, G.E., Granovsky, V.G., Metal Cutting (in Russian), Vishaya Shkola, Moscow, 1985. [16] Astakhov, V.P., Metal Cutting Mechanics, CRC Press, Boca Raton, USA, 1998. [17] Astakhov, V.P., The assessment of cutting tool wear, International Journal of Machine Tools and Manufacture, 44 (2004), 637–647. [18] Atkins, A.G., Mai, Y.W., Elastic and Plastic Fracture: Metals, Polymers. Ceramics, Composites, Biological Materials, John Wiley & Sons, New York, 1985. [19] Komarovsky, A.A., Astakhov, V.P., Physics of Strength and Fracture Control: Fundamentals of the Adaptation of Engineering Materials and Structures, CRC Press, Boca Raton, 2002. [20] Zorev, N.N., Metal Cutting Mechanics, Pergamon Press, Oxford, 1966. [21] Silin, S.S., Similarity Methods in Metal Cutting (in Russian), Moscow, Machinostroenie, 1979. [22] Kronenberg, M., Machining Science and Application. Theory and Practice for Operation and Development of Machining Processes, Pergamon Press, Oxford, 1966. [23] Gorczyca, F.Y., Application of Metal Cutting Theory, Industrial Press, New York, 1987. [24] Talantov, N.V., Physical Fundamentals of the Cutting Process, Tool Wear and Failure (in Russian), Machinostroenie, Moscow, 1992. [25] Astakhov, V.P., Outeiro, J.C., Modeling of the contact stress distribution at the tool–chip interface. In Proceeding of the 7th CIRP International Workshop on Modeling of Machining Operations, ENSAM, Cluny, France, 2004. [26] Astakhov, V.P., Tribology of metal cutting, in Mechanical Tribology. Material Characterization and Application, H.L.G.E. Totten, Editor. Marcel Dekker, New York, 2004, pp. 307–346. [27] Huq, M.Z., Celis, J.-P., Expressing wear rate in sliding contacts based on dissipated energy, Wear, 252 (2002), 375–383.

CHAPTER 5

Design of Experiments in Metal Cutting Tests

5.1 Introduction Although metal cutting is one of the oldest manufacturing processes, most essential characteristics and outcomes of this process such as tool life, cutting forces, integrity of the machined surface and energy consumption can only be determined experimentally. As a result, any further improvement in the tool, machine and process design, and implementation of new cutting tool materials are justified through a series of experimental studies. Unfortunately, experimental studies in metal cutting are very costly and time consuming requiring sophisticated equipments and experienced personnel. Therefore, the proper test strategy, methodology, data acquisition, statistical model construction and verification are of prime concern in such studies. Metal cutting tests have been carried out for at least 150 years, in tremendously increasing volume. However, most of the tests carried out so far have been conducted using a vast variety of cutting conditions and test methods having a little in common with each other. It is understood that test results are meaningless if the test conditions have not been specified in such a way that the different factors, which affect the test results, will be under a reasonable and practical degree of control. Though this sounds simple and logical, the main problem is to define and/or determine these essential factors. Unfortunately, there is lack of information dealing with test methodology and data evaluation in metal cutting tests. Some information about setup and test conditions can be found in most of the reported experimental studies. On the contrary, it is rather difficult to find corresponding information about test methodology and answers to the questions why the reported test conditions or design parameters of the setup were selected at the reported levels, what method(s) was (were) used for experimental data evaluation, etc. Although the cost of testing in metal cutting is high, there is no drive to improve or generalize the experimental results up to the level of National and International Standards. For example, the standard ANSI/ASME Tool Life Testing with Single-Point Turning Tools 276

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277

(B94.55M-1985) suggests conducting the one-variable-at-a-time test. When it comes to acquisition of test results, the only calculation of the confidence interval limits is required to carry out and report. As a result, so that only the influence of cutting speed on the tool life can be distinguished for a given machine (static and dynamic stiffness, spindle runout, accuracy of motion etc.), workpiece parameters (metallurgical state, dimensions, holding method, etc.), cutting tool material and cutting tool design. The design of experiments (DOEs) technique allows significant improvement in the methodology of machining tests. DOE is the process of planning of an experiment so that appropriate data will be collected, which are suitable for further statistical analyses resulting in valid and objective conclusions. There are a number of different methodologies of DOE; so one should select the appropriate methodology depending upon the objective of the test and the resources available. This chapter aims to discuss the basic DOE used in metal cutting tests. Particular attention is paid to least formalized stages of DOE, where the most important decisions affecting the test outcome are made. 5.2 DOE in Machining: Terminology and Requirements 5.2.1 Terminology The objective of DOE is to find the correlation between the response (for example, the cutting force, tool life, etc.) and the factors included (the parameters of the cutting process taken into consideration, for example, the cutting speed, feed, depth of cut, etc.). All the factors included in the experiment are varied simultaneously. The influence of unknown or non-included factors is minimized by properly randomizing the experiment. Mathematical methods are used not only at the final stage of the study, when the evaluation and analysis of the experimental data are conducted, but also throughout all the stages of DOE, i.e. from the formalization of a priori information till the decision-making stage. This allows answering of important questions: “What is the minimum number of tests that should be conducted? Which parameters should be taken into consideration? Which method(s) is (are) better to use in the evaluation and analysis of experimental data? [1,2].” The problem of mathematical model selection for the object under investigation requires the formulation of clear objective(s) of the study. This problem occurs in any study, but the mathematical model selection in DOE requires the quantitative formulation of the objective(s). Such an objective is called the response, which is the result of the process under study or its output. The process under study may be characterized by several important output parameters but only one of them should be selected as the response. The response must satisfy certain requirements. First, the response should be the effective output in terms of reaching the final aim of the study. Second, the response should be easily measurable, preferably quantitatively. Third, the response should be a singlevalued function of the chosen parameters.

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Input process variables are called factors. In DOE, it is necessary to take all the essential factors into consideration. Unconsidered factors change arbitrarily and increase the error of the tests. Even when a factor does not change arbitrarily but is fixed at a certain level, a false idea about the optimum can be obtained because there is no guarantee that the fixed level is the optimum one. The factors can be quantitative or qualitative but both should be controllable. Practically, it means that the chosen level of any factor can be setup and maintained during the tests with certain accuracy. The factors selected should affect the response directly and should not be a function of other factors. For example, the cutting temperature cannot be selected as a factor because it is not a controllable parameter. Rather, it depends on other process parameters like the cutting speed, feed, depth of cut, etc. The factor combinations should be compatible, i.e. all the required combinations of the factors should be physically realizable on the setup used in the study. For example, if a combination of cutting speed and feed results in drill breakage, then this combination cannot be included in the test. Often, chatter occurs at high cutting regimes that limits the combinations of the regime parameters.

5.2.2 Mathematical model One of the important stages in DOE is the selection of the mathematical model. Mathematically, the problem of DOE can be formulated as follows: define the estimation E of the response surface which can be represented by a function E{y} = φ(x1 , x2 , . . . , xk ) ,

(5.1)

where y is the process response (for example, cutting temperature, tool life, surface finish, cutting force, etc.), xi , i = 1, 2, . . . , k are the factors varied in the test (for example, the cutting edge angle, cutting speed, feed, etc.). The mathematical model represented by Eq. (5.1) is used to determine the gradient, i.e. the direction in which the response changes faster than in any other. This model represents the response surface, which is assumed to be continuous, two times differentiable, and having only one extremum within the chosen limits of the factors. In general, a particular kind of mathematical model is initially unknown due to insufficient knowledge of the phenomenon considered. Thus, a certain approximation of this model is needed. Experience shows [2] that a power series or polynomial can be selected as an approximation. The accuracy of such an approximation would depend upon the order (power) of the series. To reduce the number of tests at the first stage of the experimental study, a polynomial of the first order or a linear model is sufficiently suitable. Such a model is successfully used to calculate the gradient of the response, thus, to reach the stationary region. When the stationary region is reached then a polynomial containing terms of the second, and sometimes, the third, order may be employed.

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Experience shows [3,4] that a model containing linear terms and interactions of the first order can be used successfully in metal cutting. Such a model can be represented as # # βi xi βij xi xj (5.2) E{y} = β0 + i

ij

The coefficients of Eq. (5.2) are to be determined from the tests. Using the experimental results, one can determine the regression coefficients b1 , bi and bij , which are the estimates for the theoretical regression coefficients β1 , βi and βij . Thus, the regression equation constructed using the test results has the following form: # #  y = b0 + bi x i bij xi xj , (5.3) i

ij



where y is the estimate for E{y}.

5.2.3 Pre-process decisions Each factor selected for the DOE study has a certain global range of variation. Within this range, a local sub-range to be used in DOE is to be defined. Practically, the limits of each included factors should be set. To do this, one should use all available information such as experience, results of the previous studies, expert opinions, etc. Using this information, the approximate combination of the factors included that gives the best result should be defined. Mathematically, the defined combination can be thought of as a point in the multi-dimensional factorial space. The coordinates of this point are called the basic (zero) levels of the factors, and the point itself is termed as the zero point [1–4]. The interval of factor variation is the number which, when added to the zero level, gives the upper limit and, when subtracted from the zero level, gives the lower limit. The numerical value of this interval is chosen as the unit of a new scale of each factor. To simplify the notations of the experimental conditions and procedure of data analysis, this new scale is selected so that the upper limit corresponds to +1, lower to −1 and the basic level to 0. For the factors having continuous domains, a simple transformation formula is used xi =

x˜ i − x˜ 0 , ∆˜xi

(5.4)

where xi is a new value of the factor, x˜ i is the true value of the factor, x˜ 0 is the true value of the zero level of the factor, ∆˜xi is the interval of factor variation (in true units) and i is the number of the factor. As a result, the origin of the factorial space is shifted into a new position corresponding to zero levels of the included factors. With respect to this new coordinate system, the upper level of each factor corresponds to “+1” and the lower level to “−1.” When two factor levels are used in DOE, the design plan is designated as 2k , where k is the number of factors involved [1–3].

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Tribology of Metal Cutting

As shown, the selection of the limits of factors is the least formalized stage in DOE, so it is carried out using the experience and information available. In such a selection, the setting accuracy of factors at the chosen levels and the degree of influence of each factor on the response should be considered. One of the major objectives of such considerations is to avoid a situation where the selected interval of variation of each factor is not wide enough to detect the true influence of each factor on the response. At the stage of pre-process decisions, it is very useful to have at least an approximate idea about the curvature of the response surface. When this surface is far from a plane, the correlation between the accuracy of factors setting (requires increasing a scale unit) and the curvature of the response surface (requires reducing a scale unit) becomes significant.

5.2.4 Basic requirements to test conditions DOE requires special attention to be paid to the accuracy of the testing procedure. A relatively high variation occurred during the metal cutting tests, and low reproducibility of these tests force the experimentalist to increase the number of repetitions at the same point of the design matrix. Therefore, the first and foremost requirement is to assure minimum possible variation of the response in the test. Although there are a number of sources of errors and inaccuracies during a metal cutting test [5], it is instructive to point out some general sources in particular for practically all metal cutting tests: • Errors associated with the workpiece can be classified as the work material, mounting and clamping, and dimension related. The work material-related inaccuracies and errors stem from the variation in the mechanical, physical and microstructural variations of the work material. To reduce this source of errors, it is advisable to use the workpieces having the same mechanical and metallurgical properties preferably from the single manufacturing batch. Moreover, these properties should be tested and recorded prior to the test. When it is not possible, these properties should be requested from the steel supplier. The hardness of each workpiece should be measured prior to the test and the test should be conducted only using the workpiece where its variation does not exceed ±10%. To reduce the mounting and clamping errors, it is necessary to assure the mounting and clamping of the workpiece with the same accuracy (runout) and clamping force. The dimension-related error should be accounted when workpieces of various diameters and lengths are used. This issue is discussed in Chapter 4. • Errors associated with the cutting tool can be classified as the tool material, tool holder and tool mounting (clamping) related. The tool material (cutting insert) selected for the DOE should be from the same manufacturing batch. If it is feasible, these tools should be calibrated prior to the tests. • Errors associated with the experimental setup. Properly calibrated experimental equipments and apparatuses should be used. The test conditions should always be within the calibration ranges.

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• Errors associated with environment. To reduce the influence of slow-changing conditions (temperature of the cutting fluid, tool wear, room temperature, etc.), the test should be conducted in a randomized sequence.

5.3 Screening Test As mentioned above, probably the weakest link in DOE implementation is a set of preprocess decisions. Often, such decisions rely on experience, available information and expert opinions, and thus they are highly subjective. Even a small inaccuracy in the preprocess decisions may affect the output results dramatically. Therefore, the pre-process stage of DOE should be more formalized. Normally, any machining test includes a great number of independent variables. In the testing of gundrills, for example, there are a number of tool geometry variables (the number of cutting edges, rake angles, flank angles, cutting edge angles, inclination angles, side cutting edge back taper angle, etc.) and design variables (cutting fluid hole shape, cross-sectional area and location, profile angle of the chip removal flute, shoulder dub-off shape and location, number and location of the supporting pads, radial relief, length of the cutting tip, the shank length and diameter, etc.) that affect drill performance. However, when many factors are used in DOE, the experiment becomes expensive and time consuming. Therefore, there is always a dilemma. On one hand, it is desirable to take into consideration only a limited number of essential factors carefully selected by the experts. On the other hand, even if one essential factor is missed, the final statistical model may not be adequate to the process under study. Unfortunately, there is no simple and feasible way to justify the decisions made at the pre-process stage about the number of essential variables prior to the tests. If a mistake is made at this stage, it may show up only at the final stage of DOE when the corresponding statistical criteria are examined. Obviously, it is too late then to correct the test results by adding the missed factor. The theory of DOE offers few ways to deal with such a problem [1,2]. The first relies on the collective experience of the experimentalist(s) and the research team in the determination of significant factors. The problem with such an approach is that one or more factors could be significant or not, depending on the particular test objectives and conditions. For example, the back taper angle in gundrills is not a significant factor in drilling soft materials or cast irons, but it becomes highly significant in machining hard titanium alloys and martensitic stainless steels. A second way is to use screening DOE. This method appears to be more promising in terms of its objectivity. Various screening DOEs are used when a great number of factors are to be investigated using relatively small number of tests. This kind of test is conducted to identify the significant factors for further analysis. Fractional factorial DOE is commonly used for screening DOE [2]. Using this method, the experimentalist should be fully aware that it cannot detect any interactions among the factors involved. Unfortunately, this simple fact is misunderstood in metal cutting where such DOE has been used to study the interactions between the variables [6]. Therefore,

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if any factor interactions could be significant, this test should not be used. The author’s experience, however, shows that there are a number of significant interactions between the process parameters in metal cutting so that this DOE can hardly be acceptable in metal cutting. Plackett and Burman [7] developed a special class of fractional factorial experiments that includes interactions. When this kind of DOE (referred to as the Plackett–Burman DOE) is conducted properly using a completely randomized sequence, its distinctive feature is high resolution. Despite a number of disadvantages (for example, mixed estimation of regression coefficients), this method utilizes high-contrast diagrams for the factors included in the test as well as for their interactions of any order. This advantage of the Plackett–Burman DOE is very useful in screening tests. This section presents a simple methodology of screening DOE to be used in metal cutting tests [8]. The method, referred to as the sieve DOE, has its foundation in the Plackett–Burman design ideas, an oversaturated design matrix and the method of random balance. The proposed sieve DOE allows the experimentalist to include as many factors as needed at the first phase of the experimental study and then to sieve out the nonessential factors and interactions by conducting a relatively small number of tests. It is understood that no statistical model can be produced in this stage. Instead, this method allows the experimentalist to determine the most essential factors and their interactions to be used at the second stage of DOE.

5.3.1 Background The proposed sieve DOE includes the method of random balance. This method utilizes oversaturated design plans where the number of tests is fewer than the number of factors and thus has a negative number of degrees of freedom [9]. It is postulated that if the effects (factors and their interactions) taken into consideration are arranged as a decaying sequence (in the order of their impact on the variance of the response), this will approximate a ranged exponential-decay series. Using a limited number of tests, the experimentalist determines the coefficients of this series and then, using the regression analysis, estimates the significant effects that have a high contrast in the noise field formed by the insignificant effects. The initial linear mathematical model, that included k number of factors (effects), has the following form: y = a0 + a1 x1 + · · · + ak xk + a12 x1 x2 + · · · + ak−1,k xk−1 xk + δ,

(5.5)

where a0 is the absolute term often called the main effect, ai (i = 1, k) are the coefficients of linear terms, aij (i = 1, . . . , k − 1; j = i + 1, . . . , k) are the coefficients of interaction terms and δ is the residual error of the model. Let us distinguish l as the number of insignificant factors so (k − l) is the number of significant effects (including generally both factors and interactions) can be distinguished.

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Because the insignificant effects do not have a strong impact on the response y, the model can be simplified further to y = a0 + b1 x1 + b2 x2 + · · · + bh−l xh−l + ε

(5.6)

ε = bh−l+1 + bh−l+2 xh−l+2 + · · · + bh xh + δ

(5.7)

where

and thus 2 2 σ 2 {xh−l+1 } + bh−l+2 σ 2 {xh−l+2 } · · · + bh2 σ 2 {xh } + σ 2 {δ} σ 2 {ε} = bh−l+1

(5.8)

In these equations, (k − l) significant effects are distinguished from the total number of effects k and thus l effects are considered as nose having no important impacts on the response y. It is obvious that the residual variance of the model represented by Eq. (5.8) is greater than that in Eq. (5.5), i.e. σ 2 {ε} > σ 2 {δ} and that the estimates of the coefficients of this model are mixed. Therefore, the sensitivity of the random balance method is low. However, this method is characterized by the great contrast of essential effects, which could be distinguished easily on the noisy fields formed by other effects.

5.3.2 Pre-process decisions As mentioned above, pre-process decisions include the selection of factors and their ranges. The greater the scope (cost and time) of the experiment, the greater the attention to be paid at this stage, verifying results with independent experts in the field. Unfortunately, this has not been the case in metal cutting studies, where a great number of large, midsize and even small companies (cutting tool users and suppliers, carbide manufacturers and other tool material suppliers, work material suppliers, etc.) conduct their own experimental studies, paying little attention to this important first stage. As a result, the recommendations for the machining regimes to be used are very wide that makes them impractical. The factors taken into consideration can be of a qualitative or a quantitative nature. They and their ranges should justify the following requirements: • Controllability. Practically, it means that the selected levels of each factor can be set and maintained within a reasonable range during the tests. • Independence. Each of the selected factors cannot be a function of other factors or their combination and thus affects the process directly. For example, the cutting

284

Tribology of Metal Cutting temperature cannot be considered as a factor because it depends on other factors and cannot be set and kept at a desired level independent of other cutting parameters.

• Compatibility. This requirement means that all the required (by DOE) combinations of the chosen factors should be realizable on the test setup. For example, excessive tool and/or workpiece vibration, tool shank strength or cutting edge breakage, machine limitation in terms of speed, or feed, cutting fluid pressure normally are not realizable, and this limits compatibility. These requirements set strict limits on the ranges of factors. In addition, the accuracy of setting each included factor and the accuracy of the measurement of the response should also be the subjects of special care. The rule of thumb here is to measure all the factors and the responses with the same accuracy. To assure this, a metrological matrix of the experiment should be an inherent part of any DOE in metal cutting. The metrological matrix includes the list of measuring equipments and apparatuses, their measuring ranges, the nominal measuring errors and their variations within these ranges, the calibration data, etc. Particularly in metal cutting, static and dynamic calibrations and error assessments are mandatory [5,10]. Unfortunately, it has become customary not to report these data when presenting the experimental results in metal cutting. To simplify further consideration of the sieve DOE, it is reasonable to present a practical example. Consider the use of such DOE to determine the essential factors affecting tool life in gundrilling.

5.3.3 Basic gundrill components and geometry Gundrilling is a highly developed and efficient technique for producing deep holes in a wide variety of materials from plastics, such as fiberglass and teflon, to high-strength metals, like P-20 and Inconel. The process also enables size, location and straightness accuracy where tight tolerances and fine finishes are critical [11–15]. However, successful gundrilling requires complete understanding and integration of the gundrilling system, which includes everything related to the operation: the cutting tool, machine, fixtures and accessories, workpiece, cutting fluid, programming, control and operator skill. Optimum performance is achieved when the combination of cutting speed, feed, tool geometry, carbide grade and cutting fluid parameters is selected properly. This selection depends upon the hardness, composition and structure of the workpiece, deep-hole machine conditions and the quality requirements to the drilled holes. In terms of tool type, the straight-flute gundrill is the most common (Fig. 5.1). It has a solid- or brazed-carbide tip, depending on the tool’s diameter, with an internal cutting fluid channel running through its driver, shank and tip. Gundrill manufacturers have adopted various shapes for the cutting fluid passage in the tip: either one or two circular holes or a single kidney-shaped hole. Standard gundrills produce holes from 2 to 50 mm in diameter (Dw ) and up to 100 Dw deep in one pass, with custom length roughly doubling this magnitude.

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285

Driver

Internal coolant supply channel

Tubular Shank V-Flute Chip removal channel

Tip (Tool Head)

te Flu

Len

gth

O

all ver

Len

gth

Two-Hole Tip Kidney-Hole Tip

Round-Hole Tip

Fig. 5.1. Common gundrill and its components.

The design and geometry parameters of a commonly used gundrill are shown in Fig. 5.2. The gundrill consists of a drill body having a shank 1 and a tip 2. The tip is made up of a hard wear-resistant material such as tungsten carbide. The other end of the shank incorporates an enlarged driver 3 having the machine-specific design. The shank is of tubular shape having an elongated passage 4 extending over its entire length and connects to the drilling fluid supply passage 5 in the driver. The shank has a V-shaped flute 6 on its surface which serves as the chip removal passage. The shank length depends mainly on the depth of the drilled hole as well as on the lengths of the bushing and its holder, chip box, etc. The tip is larger in diameter than the shank that prevents the shank from coming into contact with the walls of the hole being drilled. Flute 7 on the tip, which is similar in shape to flute 6, extends along the full length of the tip. This flute is bounded by side faces 8 and 9 known as the cutting face and side face, respectively. The depth of this flute is such that the cutting face 8 extends past the axis 10 (distance c) of the tip, which is also the axis of the drill body. The angle ψc between the side and cutting faces is known as the profile angle of the tip, which is usually equal or close to the V-flute profile of the shank. The terminal end of the tip is formed with the approach cutting edge angles ϕ1 and ϕ2 of the outer 11 and inner 12 cutting edges, respectively. These cutting edges meet at the drill point P. The location of P (defined by the distance md in Fig. 5.2) can be varied for optimum performance depending on the work material and the finished hole specifications. One common point grind calls for the outer angle, (ϕ1 ), to be 30◦ and the inner angle (ϕ2 ), to be 20◦ . The geometry of the terminal end largely determines the shape of the chips and the effectiveness of the cutting fluid, the lubrication of the tool, and removal of the chips. The process of chip formation is also governed by other cutting parameters such as the cutting speed, feed rate, work material, etc.

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5 j4

g

an2

3

an1

1 14

13

j1

j2 12

md

4

11

P

Ø12.1 6 2

yc

9

16

c 10 8

7

b 13 14

15

Fig. 5.2. Gundrill geometry.

The flank surface 13 having normal clearance (flank) angle αn1 is 8–20◦ is applied to the outer cutting edge 11 and the flank surface 14 having normal clearance (flank) angle equal to αn2 (normally αn2 is 8–12◦ ) is applied to the inner cutting edge 12. To assure drill-free penetration, i.e. to prevent the interference of the drill’s flanks with the bottom of the hole being drilled, the auxiliary flank 15 and shoulder dub-off 16 are ground. Their location and geometry are uniquely defined for a given gundrill.

5.3.4 Design matrix: tool life test of gundrills The test conditions were as follows: Machine – a special deep-hole gundrilling machine was used. The drive unit was equipped with a programmable AC converter to offer variable speed and feed rate control. The machine contained a high-pressure cutting fluid delivery system capable of delivering

Design of Experiments in Metal Cutting Tests

287

a flow rate up to 75 l/min and generating a pressure of 12 MPa. The stationary workpiece-rotating tool working method was used in the tests. The feed motion was applied to the gundrill. Work material – hot rolled medium carbon steel AISI 1040 was used. The actual chemical composition has been analyzed using a LECO SA-2000 Discharge-Optical Emission Spectrometer. Special metallurgical parameters such as the element counts, microstructure, grain size, inclusions count, etc, were determined using quantitative metallography. The test bars, after being cut to length (40 mm diameter, 700 mm length), were normalized to a hardness of HB 200. Gundrills – gundrills of 12.1 mm diameter were used. The material of their tips was carbide M 30. The parameters of drill geometry were kept within a close tolerance of ±0.2◦ . The surface roughness Ra of the rake and flank faces did not exceed 0.25 µm. Each gundrill used in the tests was examined at a magnification of ×25 for visual defects such as chipping, burns and microcracks. When resharpening, the tips were ground back at least 2 mm beyond the wear marks. Cutting fluid (coolant) – “Shell Garia H” cutting fluid was used in the tests. Its temperature was maintained at 27 ± 3◦ C and its purity at 10 µm. Cutting conditions – the optimal cutting speed – 110 m/min (2894 rpm), and feed rate – 90 mm/min were selected using the results of a calibration test for given work and tool materials. The principles of the first metal cutting law (discussed in Chapter 4) were used to determine the optimal cutting temperature. Tool life criteria – the average width of the flank wear land VBB = 0.4 mm was selected as the prime criterion and was measured in the tool cutting edge plane containing the cutting edge and the directional vector of prime motion. However, excessive tool vibration and/or squeal were also used in some extreme cases. Eight factors have been selected for this sieve DOE and their intervals of variation are shown in Table 5.1.

Table 5.1. The level of the factors selected for the sieve DOE. Factors

Code designation Upper level (+) Lower level (−)

Approach Approach Flank Drill point Flank Shoulder Rake Shoulder angle angle angle offset (md ) angle dub-off angle dub-off (ϕ1 ) (◦ ) (mm) (αn2 ) angle(ϕ4 ) (γ) (ϕ2 ) (◦ ) (αn1 ) location (◦ ) (◦ ) (◦ ) (◦ ) (b) (mm) x1 x2 x3 x4 x5 x6 x7 x8 45

25

25

3.0

12

45

5

4

25

10

8

1.5

7

20

0

1

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Tribology of Metal Cutting Table 5.2. Design matrix.

Experiment number 1 2 3 4 5 6 7 8 9 10 11

x1

x2

x3

Factors x4 x5

x6

x7

x8

y1

+ + − − + + − − + − +

+ + + − − − − + − + −

− + − + − + − − − + +

− − − + + − − + − + −

− + + − − + + − + + −

+ + − − + − − + − − +

− − + + − − + + + − −

7 16 11 38 18 10 14 42 9 32 6

+ − + + − + − − − − −

Tool life (min) y2 y3 18.75 11.50 11.00 21.75 13.50 21.75 14.00 25.75 20.75 15.75 17.75

11.11 11.50 11.00 16.61 13.50 14.61 14.00 16.61 20.75 15.75 10.61

The design matrix was constructed as follows: all the selected factors were separated into two groups. The first one contained factors x1 , x2 , x3 , x4 , form a half-replica 24−1 with the defining relation I = x1 x2 x3 x4 . In this half-replica, the effects of the factors and the effects of their interactions are not mixed. The second halfreplica was constructed using the same criteria. A design matrix was constructed using the first half-replica of the complete matrix and adding to each row of this replica a randomly selected row from the second half-replica. Three more rows were added to this matrix to assure proper mixing and these rows were randomly selected from the first and second half-replicas. Table 5.2 shows the design matrix constructed. As soon as the design matrix is completed, its suitability should be examined using two simple rules. First, a design matrix is suitable if it does not contain two identical columns having the same or alternate signs. Second, a design matrix should not contain columns whose scalar products with any other column result in a column of the same (“+” or “−”) signs. The design matrix shown in Table 5.2 was found suitable as it meets the requirements set by these rules. The test results are shown in column y1 as the average tool life calculated over three independent tests under the test conditions indicated.

5.3.5 Analysis Analysis of the results of sieve DOE begins with the construction of a correlation (scatter) diagram shown in Fig. 5.3. Its structure is self-evident. Each factor is represented by a vertical bar having on its left side, values (as dots) of the response obtained when this factor was positive (the upper value) while the values of the response corresponding to lower level of the factor considered (i.e. when this factor is negative) are represented by dots on the right side of the bar. As such, the scale makes sense only along the vertical axis.

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289

y 40

30 16.4 3.57

5.77

20

19.7

10.6

6.9

4.9

1.2

10

+ −

x1

+ −

x2

+ −

x3

+ −

x4

+ −

x5

+ −

+ −

x6

x7

+ −

x

x8

Fig. 5.3. Correlation diagram (first sieve).

Each factor included in the experiment is estimated independently. The simplest way to do this is to calculate the distance between the means on the left and right sides of each bar. These distances are shown on the correlation diagram in Fig. 5.3. As shown, these are the greatest for factors x1 and x4 and thus these two factors are selected for the analysis. The effects of factors are calculated using special correlation tables. A correlation table (Table 5.3) was constructed to analyze the two factors considered. Using the correlation table, the effect of each selected factor can be estimated as Xj =

y1−2 + y1−4 + · · · + y1−(n−1) y1−1 + y1−3 + · · · + y1−n − , m m

(5.9)

where m is number of ys for the factor considered assigned to the same sign (“+” or “−”). It follows from Table 5.3 that m = 2.

Table 5.3. Correlation table (first sieve). Estimated factor

+x4

$

+x1

−x1

16 18

38 42 32

y1−1 = 34

y1−1 = 17

$

Estimated factor

+x4 y1−2 = 112

y1−2 = 37.3

$

+x1

−x1

7 10 9 11

11 14

y1−3 = 37

y1−3 = 9.3

$

y1−4 = 25

y1−4 = 12.5

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The effects of the selected factors were estimated using data in Table 5.3 and Eq. (5.10) as X1 =

y1−1 + y1−3 y + y1−4 17 + 9.3 37.3 + 12.5 − 1−2 = − = −11.75 2 2 2 2

(5.10)

X4 =

y1−1 + y1−2 y + y1−4 17 + 37.3 9.3 + 12.5 − 1−3 = − = 16.25 2 2 2 2

(5.11)

The significance of the selected factors is examined using the Student’s t-criterion, calculated as    y1−1 + y1−3 + · · · + y1−n − y1−2 + y1−4 + · · · + y1−(n−1) t= , $ 2 i si /ni 

(5.12)

where si is the standard deviation of ith cell of the correlation table defined as " si =

$

2 i yi

ni − 1

$ −

i yi

2

ni (ni − 1)

(5.13)

,

where ni is the number of terms in the cell considered. The Student’s criteria for the selected factors are calculated using the results presented in the auxiliary table (Table 5.4) as follows:    y1−1 +y1−3 − y1−2 +y1−4 (17+9.3)−(37.3+12.5) tX1 = = = −6.68 $ 3.52 2 s /n i i i 

 tX4 =

   y1−1 +y1−2 − y1−3 +y1−4 (17+37.3)−(9.3+12.5) = = 9.23 $ 3.52 2 /n s i i i

(5.14)

(5.15)

Table 5.4. Calculating t-criterion. Cell number 1 2 3 4

$

y1−i

34 112 37 25

$

y1−i

1156 12544 1369 625

2

$

2 y1−i

580 4232 351 317

ni

s2

s2 /ni

2 3 4 2

2.00 25.33 2.92 4.50

1.00 8.44 0.73 2.25

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291

A factor is considered to be significant if tx > tcr , where the critical value, tcr for the Student’s criterion is found in a statistical table for the following number of degrees of freedom # fr = ni −k = 11−4 = 7, (5.16) i

where k is the number of cells in the correlation table. For the case considered, t99.9 = 5.959 (Table 5.7 in [16]) so that the factors considered are significant with a 99.9% confidence level. The procedure discussed is the first stage in the proposed sieve DOE and thus it is referred to as the first sieve. This first sieve allows the detection of the strongest factors, i.e. those factors that have the strongest influence on the response. After these strong linear effects are detected, the size of “the screen” to be used in the consecutive sieves is reduced to distinguish less strong effects and their interactions. This is accomplished by the correction of the experimental results presented in column y1 of Table 5.2. Such a correction is carried out by adding the effects (with the reverse signs) of the selected factors (Eqs. (5.11) and (5.12)) to column y1 of Table 5.2, namely, by adding 11.75 to all the results at level “+x1 ” and −16.25 to all the results at level “+x4 .” The corrected results are shown in column y2 of Table 5.2. Using the data from this table, one can construct a new correlation diagram shown in Fig. 5.4, where, for simplicity, only a few interactions are shown although all possible interactions have been analyzed. Using the approach described above, a correlation table (second sieve) was constructed (Table 5.5) and the interaction x4 x8 was found to be significant. Its effect is X48 = 7.14. After the second sieve, column y3 was corrected by adding the effect of X48 with the opposite sign, i.e. −7.14 to all the results at level +x48 . The results are shown in

y 25

20 4.54

6.82

5.07

15

10 + −

x1

+ −

x2

+ −

x3

+ −

x4

+ −

x5

+ −

x6

+ −

x7

+ −

x8

+ −

x3x7

+ −

x1x6

Fig. 5.4. Correlation diagram (second sieve).

+ −

+

−

x4x8 x2x3x5

x

292

Tribology of Metal Cutting Table 5.5. Correlation table (second sieve). +x3 x7

−x3 x7

+x4 x8

−x4 x8

11.5 11

18.75 25.75

y2−1 = 22.5 y2−1 = 11.25

18.75 25.75 15.75 $ y2−2 = 60.25 y2−2 = 20.08

y2−3 = 44.5 y2−3 = 22.25

11.5 11 15.75 $ y2−4 = 38.25 y2−4 = 12.75

+ x3 x7

−x3 x7

+x4 x8

−x4 x8

14 20.75 $ 17.75 y2−5 = 52.5 y2−5 = 17.5

21.75 13.5 $ 21.75 y2−6 = 57 y2−6 = 19

21.75 21.75 $ 17.75 y2−7 = 61.25 y2−7 = 20.42

13.50 14 $ 20.75 y2−8 = 48.25 y2−8 = 16.08

Estimated factor

+x2

$

Estimated factor

−x2

$

column y3 of Table 5.2. Normally, the sieve of the experimental results continues while all the remaining effects and their interactions become insignificant, at say a 5% level of significance if the responses were measured with high accuracy and a 10% level if not. In the case considered, the sieve was ended after the third stage because the analysis of these results showed that there are no more significant factors or interactions left. Figure 5.5 shows the scatter diagram of the test discussed. As shown in the figure, the scatter of the analyzed data reduces significantly after each sieve, so normally three sieves are sufficient to complete the analysis.

40

Tool life, min

30

20

10 y1

y2

y3

Fig. 5.5. Scatter diagram.

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293

Table 5.6. Summary of the sieve test. Stage of sieve

Distinguished factor

Original data

x1 x4 x48 –

First sieve Second sieve

Effect −11.5 16.25 7.14 –

t-Criterion 6.68 9.23 4.6 –

The results of the proposed test are summarized in Table 5.6. Figure 5.6 shows the significance of the effects distinguished in terms of their influence on tool life. As shown, two linear effects and one interaction having the strongest effects were distinguished. The negative sign of x1 shows that tool life decreases when this parameter increases. The strongest influence on tool life has the drill point offset md . While the linear effects distinguished are known to have strong influence on tool life, the interaction x4 x8 distinguished has never before been considered in any known studies on gundrilling.

5.3.6 Concluding remarks The proposed sieve DOE allows experimentalists to take into consideration as many factors as needed. Conducting a relatively simple sieve test, the significant factors and their interactions can be distinguished objectively and then used in the subsequent full DOE. Such an approach allows one to reduce the total number of tests dramatically without losing any significant factor or factor interaction. Moreover, interactions of any order can be easily analyzed. The proposed correlation diagrams make such an analysis simple and self-evident.

18

Effect

12

6

0

−

x4

x1

x4x8

x5

x6

x2

etc.

Fig. 5.6. Significance of the effects distinguished by the sieve DOE (Pareto analysis).

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Three factors are found to have a significant effect on tool life in gundrilling. As was expected, the strongest influence has the drill point offset md . It was also found that tool life decreases when the approach angle of the outer cutting edge increases. The interaction x4 x8 distinguished has never before been considered in the known analyses on tool life in gundrilling. Using this factor and results of the complete DOE, a new geometry of gundrills has been developed. 5.4 2k Factorial Experiment, Complete Block This type of experiments are utilized to investigate the effects of one or more factors on the response. When an experiment involves more than one factor, these factors can influence the response individually as well as jointly. In the case of one factor-at-a time experiment, the selected experimental methodology does not allow proper assessment of the joint effects of the factors involved. Factorial experiments conducted in completely randomized designs are especially useful for evaluating the joint factor effects. Factorial experiments include all possible factor combinations in the experimental design. Completely randomized designs are appropriate when there are no restrictions on the order of testing. The mathematical description of the object under study in the vicinity of zero point can be obtained by varying each factor at two levels distinguished from the zero level by the interval of variation. When the experiment includes all possible non-repeated factorlevel combinations, it is called as the complete block. The number of such combinations is N = 2k .

5.4.1 Regression model and design matrix Consider the case where three factors are taken into consideration. As such we deal with 23 factorial experiment that demonstrated its usefulness in metal cutting tests [3,9]. The regression equation for this test is 3 3 # # %& y = E y = b0 + bi x˜ i + bij x˜ i x˜ j +b123 x˜ 1 x˜ 2 x˜ 3



i=1

(5.17)

i,j=1

The complete block enables one to obtain the separate (non-mixed) estimates for all coefficients b of this model. This is the major advantage of this type of DOE. Obtaining the mathematical model in the form of Eq. (5.18) includes the following stages: • Design of experiment: statement of the problem; selection of the response and factors to be involved; determining the levels of the factors, selection of the sequence of the factor-level combinations – construction of the design matrix; selection

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295

Table 5.7. Treatment combinations and effects in 23 factorial experiment. Point of matrix (u)

x0

x1

x2

x3

x1 x2

x1 x3

x2 x3

x1 x2 x3

1 2 3 4 5 6 7 8

+ + + + + + + +

− + − + − + − +

− − + + − − + +

− − − − + + + +

+ − − + + − − +

+ − + − − + − +

+ + − − − − + +

− + + − + − − +

of the number of observations to be taken at each point of the design matrix; selection of a regression model to describe the experimental results. • Experiment itself as a series of tests; data collection in each test. • Evaluation and analysis: examination of the statistical significance of the model coefficients; examination of the homogeneity of the row variances; examination of the adequateness of the mathematical model obtained. Using the code values (+1, −1), the experimental conditions can be written as the design matrix, where the rows correspond to different tests and the columns correspond to the different code values of the factors [2]. The design matrix for a 23 factorial experiment (complete block) is shown in Table 5.7. In this table, columns x1 , x2 and x3 form the design matrix because they directly set up the test conditions. Further to the right, the columns for interactions x1 x2 , x1 x3 , x2 x3 and x1 x2 x3 are placed. These are to be used for the estimation of the factor interactions. A pseudo-variable x0 is also added for the estimation of coefficient b0 . The value of x0 (+1) is the same in all rows. The design matrix described can be represented graphically, as shown in Fig. 5.7. New coordinate axes x1 , x2 , x3 are drawn through the origin 0 parallel to the original axes of the factors. The origin 0 corresponds to the basic (zero) level of the factors. The scale of the new coordinate system is selected so that the intervals of variation of each factor are equal to 1. Therefore, the design is a cube with the eight runs forming the corners of the cube, as shown in Fig. 5.7. The following notation of tests is normally used. A number u (u = 1, 2, ..., 8) is attributed to each point in the design matrix. The tests have double numbering, the first number shows the point in the design matrix; the second is a number of the repetition in this point. The number of repetitions at the same point is designated by ru (ru > 1). For example, y23 is the response obtained in the third test conducted at the second point of the design matrix. 5.4.2 Properties of 2k factorial experiment, complete block There are several important properties of a complete block design matrix making this matrix very suitable for obtaining the mathematical models using the experimental data.

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Tribology of Metal Cutting

x2 4

3 7

+1

8 0

x2

−1

x3

x1

1 2 5 −1

+1

6

+1

−1

x1 x3 Fig. 5.7. Graphical representation of the 2k design.

First two directly stem from the way the matrix is constructed. The first property is the matrix symmetry relative to the center of the experiment. It can be described as follows: the sum of elements of each vector-column (except that for x0 ) is equal to zero, i.e. m #

xiu = 0,

i = 1,2,...,2k −1,

(5.18)

u=1

where u, m are the number of a point and the total number of points in the matrix, respectively. The second property is that the sum of squares of the element of each vector-column is equal to the number of the points in the matrix, i.e. m #

2 xiu = m,

i = 1,2,...,2k −1

(5.19)

u=1

The third property is called the orthogonality of the design matrix. Orthogonality in such a context means that the sum of the product of entries of any two vector-columns in the matrix is equal to zero, i.e. m # u=1

xiu xju = 0,

i = j,

i,j = 1,2,...,2k −1

(5.20)

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297

Therefore, the design matrix normal system is a diagonal system. Another important consequence of this property is the mutual independence of the estimated value of the regression coefficients that significantly simplifies their calculations. The model considered is linear with respect to the response but non-linear with respect to the factors. The non-linearity in such a context means that the interactions of the factors are taken into consideration so that they can be estimated quantitatively. Only when bij = 0 and b123 = 0, then the resultant model is linear with respect to both the factors and interactions. If a model is non-linear then one should realize that its non-linearity shows up in the dependence of a factor on the level of other factor, i.e. interaction of these two factors takes place. The complete block DOE allows quantitative evaluation of such interactions. The complete block 23 DOE allows to obtain evaluations for eight regression coefficients b0 , b1 , b2 , b3 , b12 , b13 , b23 and b123 . However, if one tries to obtain the regression coefficients of the squared factors (b11 , b22 , etc.) of regression then one finds that it is not possible because columns x12 , x22 and x32 coincide with each other and with x0 . Because these columns become indistinguishable, it is impossible to say what b0 estimates in this case.

5.4.3 Example 1: experimental study of the roughness and roundness of the drilled holes Obtaining the mathematical model. Consider the use of DOE in the experimental study of the influence of three parameters: cutting speed ν(x1 ), feed f (x2 ) and the cutting fluid flow rate Q(x3 ) on the roughness ∆(y1 ) and roundness ρ(y2 ) of the machined hole in gundrilling. A 23 DOE, complete block is used. According to Eq. (5.18), the mathematical model for this case can be written as follows: 

y = b0 +b1 x1 +b2 x2 +b3 x3 +b12 x1 x2 +b13 x1 x3 +b23 x2 x3 +b123 x1 x2 x3

(5.21)

The levels of the factors and intervals of factor variations are shown in Table 5.8. At each point of the design matrix (Table 5.7), the tests were replicated three times (r = 3). The sequence of the tests was arranged using a generator of random numbers. The experimental results for roughness and for roundness are shown in Tables 5.9 and 5.10, respectively. The orthogonality of the design matrix simplifies the calculation of the regression coefficients, which can be calculated as $m bi =

u=1 xiu yu

m

,

(5.22)

where i = 1, 2, ..., k is the number of factor, m is the number of points of the design matrix m = 8 and yu is the mean response at point u of the design matrix (averaged

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Table 5.8. The levels of factors and their intervals of variation (roughness and roundness tests). Levels of factors

Notation

ν(m/min) (n(rpm)) x1

x2

x3

0

100 (1670.92) 15 (250.64) 115 (1921.56) 85 (1420.28)

0.07 (116.96) 0.02 (101.93) 0.09 (172.94) 0.05 (71.01)

60 (16) 20 (5.33) 80 (21.33) 40 (10.67)

Basic Interval of variation

∆xi

Upper

+1

Lower

−1

f (mm/rev) (fm (mm/min))

Q(l/min) (G(min))

Table 5.9. Test results (roughness of machined holes (µm)). u

y1

y2

y3

Average response yu

Row variance su2

1 2 3 4 5 6 7 8

0.57 0.44 0.34 0.22 0.93 0.22 0.17 0.33

0.44 0.38 0.21 0.49 0.49 0.47 0.24 0.21

1.00 0.42 0.15 0.22 0.20 0.21 0.17 0.32

0.67 0.41 0.23 0.31 0.54 0.30 0.19 0.29

0.0859 0.0009 0.0095 0.0243 0.1351 0.0217 0.0017 0.0044

s2 {y}

8 $ u=1

su2 /8 = 0.03543

Table 5.10. Test results (roundness of machined holes (µm)). u

y1

y2

y3

Average response yu

Row variance su2

1 2 3 4 5 6 7 8

4.000 4.000 4.500 3.000 5.500 3.200 3.500 4.500

2.900 2.300 4.900 1.200 4.000 3.500 2.200 2.500

5.300 2.600 6.000 4.200 5.200 3.000 3.000 2.500

4.067 2.967 5.133 2.800 4.900 3.233 2.900 3.167

1.508 0.832 0.603 4.560 0.603 0.063 0.430 1.333

s2 {y}

8 $ u=1

su2 /8 = 1.245

Design of Experiments in Metal Cutting Tests

299

over r repetitions) as $r yu =

j=1 yuj

ru

=

y1 +y2 +y3 3

(5.23)

Because each factor (except for x0 ) is varied at two levels (+1 and −1), the calculations are done by attributing to the entries of column yu the signs of the entries of the column for the corresponding factor, followed by algebraic summation of these entries. A regression coefficient is obtained by dividing the results by the number of plan point. In the case examined $m b1 =

u=1 x1u yu

m

1 = (−0.67+0.41−0.23+0.31−0.54+0.30−0.19+0.29) 8 = −0.04125

$m b2 =

u=1 x2u yu

m

1 = (−0.67−0.41+0.23+0.31−0.54−0.30+0.19+0.29) 8 = −0.1125

$m b3 =

u=1 x3u yu

m

1 = (−0.67−0.41−0.23−0.31+0.54+0.30+0.19+0.29) 8 = −0.0375

$m b12 =

u=1 x12u yu

m

1 = (0.67−0.41−0.23+0.31+0.54−0.30−0.19+0.29) 8 = 0.0850

$m b13 =

u=1 x13u yu

m

1 = (0.67−0.41+0.23−0.31−0.54+0.30−0.19+0.29) 8 = 0.0050

$m b23 =

u=1 x23u yu

m

1 = (0.67+0.41−0.23−0.31−0.54−0.30+0.19+0.29) 8 = 0.0225

300

Tribology of Metal Cutting $m

b123 =

u=1 x123u yu

m

1 = (−0.67+0.41+0.23−0.31+0.54−0.30−0.19+0.29) 8 = 0.0000

Calculation of b0 is conducted using the same rule $m b0 =

u=1 x0u yu

m

1 = (0.67+0.41+0.23+0.31+0.54+0.30+0.19+0.29) 8 = 0.3675

Substituting these calculated regression coefficients into Eq. (5.22), one obtains a mathematical model in the transformed variables as y = 0.3675−0.0412x1 −0.1125x2 −0.0375x3 + 0.0850x1 x2 −0.0050x1 x3 +0.0225x2 x3

(5.24)

Statistical examination of the results obtained. Because DOE emanates from the statistical nature of the process considered, the mathematical model obtained should be analyzed carefully. The objective of this analysis is dual: on one hand it is necessary to extract the maximum information from the collected data; on the other hand, the reliability and accuracy of the results obtained should be verified. The following procedure for the examination of experimental data has been developed for metal cutting studies: Calculation of the row variance and the variance of the response. The result of each test run contains certain test error which is lowered by conducting the test several times (ru ) under the same test conditions, i.e. in each row of the test matrix. The row variances are calculated using the data from Table 5.9 as 

$r j=1

su2 =

yuj −yu

2 (5.25)

ru −1

The results are shown in Table 5.9. The variance of the response, s2 {y}, is the arithmetic average of m different variants of tests (that is the average variance); in other words $m

$m s {y} = 2

2 u=1 su

m

=

2 u=1 su

$r j=1



yuj −yu

m(r −1)

2 (5.26)

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The calculation of the variance of the response, s2 {y}, is shown in Table 5.9. The calculated variance is valid only when the raw variances are homogeneous. Examination of the variance homogeneity. Because the errors obtained in the experimental data in machining tests have normal distribution, the homogeneity test is conducted using the statistical criteria of Fisher (F-criterion), Cochran and Bartlett. Although the F-criterion is widely used for this purpose, one should remember that, in general, it cannot be used when the number of variances under study is more than two because this criterion takes into consideration only the maximum and minimum variances and thus ignores the others. When the number of test repetitions at each point of the design matrix is the same for all points, the Cochran’s criterion should be used 2 instead. This criterion is calculated as the maximum variance smax to the sum of all variances. In the case considered Gexp =

0.1352 = 0.47 0.2834

(5.27)

Using the table of Cochran numbers [17], the critical Cochran number is found to be Gcr = 0.61 for the degrees of freedom for the maximum variance f1 = ru −1 = 3−1 = 2 and the total degree of freedom of the variance f2 = m×r = 8×3 = 24 at 5% level of significance. Because Gexp < Gcr , the variances are considered to be homogeneous. Examination of the significance of the model coefficients. Significance testing of each model coefficient is evaluated independently using the t-criterion (Student’s criterion). When using the complete factorial experiment, the confidence intervals for all the coefficients of the model should be of equal width. First, the variance of regression coefficient, s2 {bi } is to be determined. When the number of repetitions (ru ) is the same for each point of the design matrix, this variance can be calculated using the following formula: s2 {bi } =

s2 {y} mru

(5.28)

with fE = m(ru −1), the number of degrees of freedom. In the case considered, s2 {bi } = 0.03543/8·3 = 1.46×10−3 or s{bi } = 0.038 Next step is to calculate the t-criterion for each model coefficient as ti =

|bi | s{bi }

(5.29)

In the considered case: t0 = 9.67, t1 = 1.05, t2 = 2.96, t3 = 0.99, t12 = 2.24, t13 = 0.13 and t23 = 0.59. The critical value of the t-criterion, tcr is determined with fE = m(ru −1) = 8(3−1) = 16 degrees of freedom at a significant level of α = 5% using the statistical tables. It was found that tcr = 1.74. If ti < tcr then coefficient bi is considered to be insignificant and thus bi = 0. In the case considered, coefficients b1 , b3 , b13 and b23 are found to be insignificant.

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The confidence interval for each significant coefficient can also be determined as having length 2∆bi where ∆bi = tcr s {bi } = 1.74×0.038 = 0.06612

(5.30)

As shown, all the coefficients have the same confidence interval. Coefficient bi is considered to be significant if its absolute value is more than half of the confidence interval, i.e. when |bi | > ∆bi . The comparison of the results of Eq. (5.31) with the absolute values of the remaining coefficients shows that they all are still significant. The mathematical model can be re-written now including only the significant coefficients 

y = 0.3675−0.1125x2 +0.085x12

(5.31)

To obtain the model in real value of variables, it is necessary to substitute the transformation given by Eq. (5.4) into Eq. (5.32)



y = 0.3675−0.1125

ν−100 ν−100 f −0.07 +0.085 15 15 0.02

(5.32)

or finally 

y = 2.7446−0.0198ν−33.9583f +0.2833νf

(5.33)

Equation (5.34) reveals that for the selected upper and lower limits of the factors, the surface roughness in gundrilling depends not only on the cutting speed and feed singly, but also on their interaction. As follows from the foregoing analysis, the cutting fluid flow rate is found to be an insignificant parameter for the selected limits of this factor. It is a common problem at this stage of the statistical analysis that a particular factor (and the corresponding regression coefficient), which was thought to be significant before testing, is found to be insignificant. This situation might occur due to the following: • The selected zero level x˜ i0 is too close to the point of a local extremum of factor x˜ i so that bi =

  ∂ y x˜ i0 =0 ∂x˜ i

(5.34)

• The selected interval of variation ∆˜xi is not sufficiently wide to detect the influence of this factor on the response. • Factors and/or interaction corresponding to the regression coefficient under consideration do not have a functional relationship with the response.

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• The large error occurred during the test is due to the presence of uncontrollable variables. When it is believed that the factor being considered has a significant influence on the response, then: • The basic (zero) value of the factor should be changed. • The interval of factor variation should be increased. • The experiment should be repeated with reduced errors due to uncontrollable variables. In the case considered, the influence of cutting fluid flow rate (Q) is found to be insignificant. This can be explained by a narrow range of the interval of variation of this factor. But this interval cannot be increased because its upper limit is restricted by the cutting fluid pressure available in the machine while its lower limit is restricted by reliable chip removal. Therefore, it can be concluded that the cutting fluid flow rate does not affect the roughness of the machined hole within the realizable working regimes. Adequacy of the model. The next step is to check the adequacy of the model obtained. To do that, the differences between the predicted responses by the obtained model and the mean of the experimentally obtained responses at each point of the design matrix should be determined and analyzed. These differences are used to calculate the residual 2 ). When the number of repetitions (r ) is the same variance, or variance of adequacy (sad u at each point of the design matrix then ru #  (¯y − y u )2 , m−n m

2 Sad =

(5.35)

u=1

where n is the number of terms in Eq. (5.34) including the free term, yu is the mean  response at u row of the design matrix and y u is the response at the same point calculated using Eq. (5.34). The variance of adequacy is determined with the following degrees of freedom fad = m−n = 8−4 = 4

(5.36)

The examination of the model adequacy includes the computation of the ratio “the vari2 )/the variance of the response (s2 {y}).” The procedure includes the ance of adequacy (sad use of the F-criterion of Fisher as F=

s sad s2 {y}

(5.37)

If the calculated value of F < Fcr , where Fcr is determined from the statistical table for F-criterion under fad degrees of freedom and the selected level of significance (α%), then the model is considered as adequate. Otherwise, the model is considered

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2 ) does not exceed variance of the to be inadequate. If the variance of adequacy (sad response (s2 {y}), then F ≤ 1 so F < Fcr is valid for any degrees of freedom.

In the case considered

2 3×0.0282 r #  yu − y u = = 0.01692 m−n 8−3 m

2 sad =

(5.38)

u=1

2 < s2 {y} (0.01692 < 0.03543), the model adequacy is Because in the case considered sad obvious even without using the F-criterion calculations.

The examination of the model adequacy is possible only when fad > 0, i.e. when the number of estimated coefficients of the model (n) is less than the number of the points in the design matrix (m). If, however, n = m then fad = 0, i.e. no degrees of freedom left to check the adequacy of the model. Experience, however, shows that fortunately in practice, some regression coefficients are always found to be insignificant [9]. Using the above-described procedure and data from Table 5.10, the following mathematical model for the roundness of the gundrilled hole is obtained ∆R(µm) = −20.044+0.238ν+396f +0.462Q−3.960νf −0.005νQ−6.600fQ+0.066νfQ

(5.39)

As shown, the roundness (surface finish) of the drilled holes depends not only on the regime parameters but also on their interactions. Even though the cutting speed, feed and cutting fluid flow rate have significant influence of roundness, they cannot be judged individually due to their interactions.

5.4.4 Example 2: tool life and cutting forces There are certain cases in metal cutting experiments, where the mathematical models of the response have special formats widely accepted and used in literature [18,19]. Some of these formats may not be fully suitable for the statistical analysis. Therefore, a certain transformation of a particular model to bring it into a format acceptable for DOE might be necessary. The best example is the tool life model, which normally has the following form: T = Cνx f y dwz ,

(5.40)

where T is tool life (min) and C is a constant mainly attributed to the properties of the work material. If Eq. (5.41) is selected as a mathematical model of the response, then in order to apply the described methods of DOE, some transformation of this equation is needed. Taking

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305

the logarithms of both sides of this equation, a new mathematical model is obtained as E{T } = β0 +β1 x1 +β2 x2 +β3 x3 ,

(5.41)

where E{T } is the mathematical expectation of true tool life in the logarithmic scale, x1 ,x2 and x3 are logarithms of ν,f and dw , respectively, and β0 ,β1 ,β2 and β3 are coefficients to be statistically estimated. It should be explained here that the transformation described is not very strict from the statistical viewpoint. First, it is not clear what happens to the experimental error included in the original model. Second, the estimates for the coefficient can be biased [2]. Third, if the errors in Eq. (5.42) are multiplicative, then no problem can be expected. However, if these errors are additive, there could be a problem if the experimentalist tries to isolate the error term. Nonetheless, the practice of metal cutting studies has shown that such a transformation may be accepted in most practical cases. The regression equation for Eq. (5.42) can be written as 

y = b0 +b1 x1 +b2 x2 +b3 x3 ,

(5.42)



where y is the estimator for E{T } in Eq. (5.42), b0 ,b1 ,b2 and b3 are the estimators for β0 ,β1 ,β2 and β3 , respectively. Equation (5.43) is an empirical model of tool life. To determine the model coefficients, a 23 factorial DOE can be used. If expression 1 (ln ximax −ln ximin ) 2

(5.43)

is selected to be a new scale unit then the transformation of the true values of the factor x˜ i to the transformed value of this factor (xi ) will be basically the same as before (Eq. (5.4)) xi =

2(ln xi −ln ximax ) +1 ln ximax −ln ximin

(5.44)

The results of the coordinate transformations are shown in Table 5.11. In this table, dw is the width of the outer cutting edge. The design matrix and the experimental results are shown in Table 5.12. Repeating the above-discussed procedure, the regression equation was obtained as 

y = 4.04−0.96x1 −0.29x2 +0.13x3

(5.45)

The statistical data evaluation should be conducted in a specific sequence. First of all, one need to verify that the equation of the first order (Eq. (5.46)) is statistically sufficient to describe the phenomenon under study. To do this, the null hypothesis should $ be verified, i.e. it has to be checked out that the sum of all regression coefficients i βii

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of the second order terms xi2 is equal to zero. For the case under consideration: b0 = 4.04; the mean response at the zero-level (point No. 9 of the matrix (Table 5.12)) is y0 = 4.27; the variance of the response s2 {y} = 0.25. Then b0 −y0 = 4.04−4.23 < s2 {y}. Therefore, the quadratic effects are statistically negligible. Substituting Eq. (5.45) into Eq. (5.46) one can obtain y = 9.55−1.37ln x1 −0.41ln x2 +0.19ln x3

(5.46)

or in the common exponential form T=

e9.55 dw0.19 ν1.37 f 0.14

(5.47)

Table 5.11. Levels of factors and their intervals of variation (tool life and cutting force tests). Levels of factors

Notation

Basic Interval of variation Upper (+) Lower (−)

0 ∆xi +1 −1

V (m/min) x1 125 75 200 50

f (mm/rev)

ln x1 4.83 4.32 5.30 3.91

x2 0.125 0.075 0.200 0.050

dw (mm)

ln x2 −2.08 −2.59 −1.61 −3.00

x3 ln x3 2.5 0.92 2.0 0.69 4.5 1.5 0.5 −0.69

Table 5.12. Design matrix and experimental results (tool life test). Point

x0

x1

x2

Tool life (T) (min) (ln T)

x3

1

+

−

−

−

2

+

+

−

−

3

+

−

+

−

4

+

+

+

−

5

+

−

−

+

6

+

+

−

+

7

+

−

+

+

8

+

+

+

+

9

1

0

0

0

bi

4.04

−0.96

−0.29

0.13

y1

y2

y3

y

95.0 4.55 25.0 3.22 135.0 4.90 14.0 2.64 162.0 5.08 45.0 3.80 143.0 4.96 10.0 2.30 124.0 4.81

156.0 5.04 31.0 3.43 129.0 4.85 16.0 2.77 264.0 5.57 78.0 4.35 215.0 5.36 8.0 2.08 68.0 4.22

132.0 4.88 23.0 3.12 85.0 4.44 22.0 3.09 185.0 5.21 40.0 3.69 170.0 5.13 12.0 2.48 45.0 3.80

128.0 4.82 26.3 3.26 116.3 4.75 17.3 2.83 203.6 5.29 54.3 3.95 176.0 5.15 10.0 2.30 79.0 4.27

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307

Table 5.13. Experimental results for cutting force components. Cutting edge number

Statistical relationships for the cutting force components Fx (N)

Fy (N)

Fz (N)

1 2 3

1497t 0.98 f 0.81 1560t 0.98 f 0.78 1620t 0.94 f 0.77

450t 1 f 0.81 585t 1.07 f 0.96 770t 0.92 f 0.90

594t 0.94 f 0.61 636t 0.93 f 0.66 728t 0.93 f 0.63

The same approach was used to obtain the equations for the cutting force components (Table 5.13) acting on each part of the drill (3 cutting edges having width dw1 ,dw2 and dw3 ).

5.5 Group Method of Data Handling 5.5.1 Background Group Method of Data Handling (GMDH) was applied in a great variety of areas for data mining and knowledge discovery, forecasting and systems modeling, optimization and pattern recognition [20–23]. Inductive GMDH algorithms provide a possibility to find interrelations in data automatically, to select the optimal structure of model or network and to increase the accuracy of existing algorithms. This original selforganizing approach is substantially different from deductive methods commonly used for modeling. It has inductive nature – it finds the best solution by sorting-out possible alternatives and variants. By sorting different solutions, the inductive modeling approach aims to minimize the influence of the experimentalist on the results of modeling. An algorithm itself can find the structure of the model and the laws, which act in the system. It can be used as an advisor to find new solutions of artificial intelligence (AI) problems. GMDH is a set of several algorithms for different problems solution. It consists of parametric, clusterization, analogs complexing, rebinarization and probability algorithms. This self-organizing approach is based on the sorting-out of models of different levels of complicity and selection of the best solution by a minimum of external criterion characteristic. Not only polynomials but also non-linear, probabilistic functions or clusterizations are used as basic models. In the author’s opinion, the GMDH approach is the most suitable for metal cutting studies because: • The optimal complexity of model structure is found, adequate to the level of noise in the data sample. For real problems solution with noisy or short data, simplified forecasting models are more accurate. • The number of layers and neurons in hidden layers, model structure and other optimal neutral network (NN) parameters are determined automatically.

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• It guarantees that the most accurate or unbiased models will be found – method does not miss the best solution during the sorting of all variants (in a given class of functions). • Any non-linear functions or features can be used as input variables, which can influence the output variable. • It automatically finds interpretable relationships in data and selects effective input variables. • GMDH sorting algorithms are rather simple for programming. • The method uses information directly from the data samples and minimizes the influence of a priori researcher assumptions about the results of modeling. • GMDH neuronets are used to increase the accuracy of other modeling algorithms. • The method allows finding an unbiased physical model of object (law or clusterization) – one and the same for all future samples. There are many published articles and books devoted to GMDH theory and its applications. The GMDH can be considered as a further propagation or extension of inductive self-organizing methods to the solution of more complex practical problems. It solves the problem of how to handle the data samples of observations. The goal is to obtain a mathematical model of the object under study (the problem of identification and pattern recognition) or to describe the processes, which will take place at the object in the future (the problem of process forecasting). GMDH solves, by means of a sorting-out procedure, the multidimensional problem of model optimization   g = arg min CR(g) CR(g) = f P,S,z2 ,T1 ,V , (5.48) g⊂G

where G is a set of models considered, CR is the external criterion of the model g quality from this set, P is the number of variables set, S is model complexity, z2 is the noise dispersion, T1 is the number of data sample transformation and V is the type of reference function. For the definite reference function, each set of variables corresponds to definite model structure P = S. Problem transforms to much simpler one-dimensional CR(g) = f (S)

(5.49)

when z2 = constant, T = constant and V = constant The method is based on the sorting-out procedure, i.e. consequent testing of models, chosen from a set of model candidates in accordance with the given criterion. Most of the GMDH algorithms use the polynomial reference functions. General correlation between the input and output variables can be expressed by Volterra functional series, discrete analog of which is Kolmogorov–Gabor polynomial y = b0 +

M # i=1

bi xi +

M M # # i=1 j=1

bij xi xj +

M # M M # # i=1 j=1 k=1

bijk xi xj xk ,

(5.50)

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309

where X(x1 , x2 ,...,xM ) is the input variables vector, M is the number of input variables and A(b1 , b2 , ..., bM ) is the vector of coefficients. Components of the input vector X can be independent variables and functional forms or finite difference terms. Other non-linear reference functions, such as difference, probabilistic, harmonic and logistic can also be used. The method allows finding simultaneously the structure of model and the dependence of modeled system output on the values of most significant inputs of the system. GMDH, based on the self-organizing principle, requires minimum information about the object under study. As such, all the available information about this object should be used. The algorithm allows finding the needed additional information through the sequential analysis of different models using the so-called external criteria. Therefore, GMDH is a combined method: it uses the test data and sequential analysis and estimation of the candidate models. The estimates are found using relatively small part of the test results. The other part of these results is used to estimate the model coefficients and to find the optimal model structure. Although GMDH and regression analysis use the table of test data, the regression analysis requires the prior formulation of the regression model and its complexity. This is because the row variances used in the calculations (Section, Statistical Examination of the Result Obtained, Eq. (5.26)) are internal criteria. A criterion is called an internal criterion if its determination is based on the same data that is used to develop the model. The use of any internal criterion leads to a false rule: the more complex model is more accurate. This is because the complexity of the model is determined by the number and highest power of its terms. As such, the greater the number of terms, the smaller the variance. GMDH uses the external criteria. A criterion is called external if its determination is based on new information obtained using “fresh” points of the experimental table not used in the model development. This allows the selection of the model of optimum complexity corresponding to the minimum of the selected external criterion. Another significant difference between the regression analysis and GMDH is that the former allows construction of the model only in the domain where the number of model coefficients is less than the number of points of the design matrix because the examination of model adequacy is possible only when fad > 0, i.e. when the number of estimated coefficients of the model (n) is less than the number of points in the design matrix (m). GMDH allows much wider domain where, for example, the number of model coefficients can be millions and all these are estimated using the design matrix containing only 20 rows. In this new domain, accurate and unbiased models are obtained. GMDH algorithms utilize minimum experimental information on input. This input consists of a table having 10–20 points and the criterion of model selection. The algorithms determine the unique model of optimal complexity by the sorting out of different models using the selected criterion. The essence of the self-organizing principle in GMDH is that the external criteria pass their minimum when the complexity of the model is gradually increased. When a particular criterion is selected, the computer executing GMDH finds this minimum and the corresponding model of optimal complexity. As such, the value of the selected criterion referred to as the depth of minimum can be considered as an estimate of the accuracy

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and reliability of this model. If sufficiently deep minimum is not reached then the model is not found. This might take place when the input data (the experimental data from the design matrix) are: (1) noisy; (2) do not contain essential variables; (3) the basic function (for example, polynomial) is not suitable for the process under consideration, etc.

5.5.2 Example: tool life testing Design matrix. As the metal cutting process takes place in the cutting system, it depends on many system parameters whose complex interactions make it difficult to describe the system mathematically. Due to complexity of the factors’ interaction, the cutting process can be compared with “natural” processes which are known as “poorly organized.” This is because it is very difficult to establish the cause–effect links between the input and output variables of the real cutting process through direct observations of this process. That is why so many explanations for the same machining phenomena (for example, the shear bands in the chip) and theories of the cutting process exist today. The preliminary tests have shown that the cutting regime (the cutting speed (v) and feed (f )) and the parameters of the tool geometry should be considered as the input variables. Tool life is to be considered as the output parameter. Therefore, the problem is to correlate the input variables with the output parameter using a statistical model. In other words, it is necessary to find a certain function (whether linear or not)   ¯ = F x, B¯ A

(5.51)

which is continuous with respect to the vector of arguments x¯ = (¯x1 , x¯ 2 ,..., x¯ n ) each ¯ of which can be varied independently in the range [¯xmin , x¯ max ]. In Eq. (5.52), B = b¯ 1 , b¯ 2 ,..., b¯ n is the vector of the estimates for the model’s coefficients. The vector of input variables contains 11 variables (M = 11) which are (Fig. 5.8): x1 is the approach angle of the outer cutting edge (ϕ1 ), x2 is the approach angle of the inner cutting edge (ϕ2 ), x3 is the normal flank angle of the outer cutting edge (α1 ), x4 is the normal flank angle of the outer cutting edge (α2 ), x5 is the distance c1 shown in Fig. 5.8, x6 is the distance c2 shown in Fig. 5.8, x7 is the location distance of the drill point with respect to the x axis of the tool coordinate system (md ),

Design of Experiments in Metal Cutting Tests

311

x

n(m/min) c2 c1

Trailing pad

y

Drill corner

Leading pad

z

f(mm/rev)

B−B

md

A−A

C a2

a1

A B y

j2

mk

C−C

a3

j1 A

B

C Ø35.00 Fig. 5.8. Variables included in the test.

x8 is the location distance of the two parts of the tool rake face with respect to the x axis of the tool coordinate system (mk ), x9 is the flank angle of the auxiliary flank surface (α3 ), x10 is the cutting speed (v) (m/min), x11 is the cutting feed (f ) (mm/rev). The test conditions were as follows: • Machine – a special gundrilling machine was used. The drive unit was equipped with a programmable AC converter to offer variable speed and feed rate control. The machine contained a high-pressure drilling fluid delivery system capable of delivering a flow rate up to 120 l/min and generating a pressure of 12 MPa.

312

Tribology of Metal Cutting The stationary tool-rotating workpiece working method was used in the tests. The feed motion was applied to the gundrill.

• Work material – because special parts, calender bowls, were drilled, the work material was malleable cast iron, Class 80002 having the following properties: hardness, Brinell HB 241 – 285; tensile strength, ultimate (Rm) – 655 MPa; tensile strength, yield (Rp0,2) – 552 MPa; elongation at break – 2%. • Gundrills – specially designed and custom-made gundrills of 35 mm diameter were used. The material used in the cutting inserts was carbide M30. The parameters of drill geometry were kept within close tolerance of ±0.2◦ . The surface roughness Ra of the rake and flank faces did not exceed 0.25 µm. Each gundrill used in the tests was examined at a magnification of ×25 for visual defect such as chipping, burns and microcracks. When re-sharpening, the tips were ground back at least 2 mm beyond the wear marks. • Drilling fluid (coolant) – a water-soluble gundrill cutting fluid having 7% concentration. • Tool life criteria – the average width of the flank wear land VBB = 1.0 mm was selected as the prime criterion and was measured in the tool cutting edge plane containing the cutting edge and the directional vector of prime motion. However, excessive tool vibration and/or squeal were also used in some extreme cases as a criterion of tool life. The schematic of the experimental setup, shown in Fig. 5.9, is mainly composed of the deep-hole machine, a Kistler sex-component dynamometer, charge amplifiers and Kistler signal analyzer. The design matrixes used in GMDH, {¯xij } were obtained as arguments xi were selected randomly as generated by a random number generator. This assures the uniform density of probability of occurring of ith argument in jth experiment, which does not depend on the other argument in the current or previous runs. As such, the design matrix {¯xij } is considered as n realization of a random vector x¯ having normal density of distribution of paired scalar products of all factors over the columns of the design matrix due to the independence of the factors. In the algorithm of GMDH, this is assured using the Kolmogorov criterion; so the design matrix is generated using a generator of random numbers until the normal distribution is assured [20]. Five levels of the factors were selected for the study. The levels of the factors and intervals of factor variations are shown in Table 5.14. The upper level (+2) for the cutting speed, 53.8 m/min (490 rpm), was selected as a result of the preliminary testing and was limited by the dynamic stability of the shank. As such, the critical rotational speed of the shank was determined to be 618rpm. The design matrix shown in Table 5.15 was obtained using the algorithm described in [20]. Dynamic phenomena. Before any DOE and/or optimization technique is to be applied, one has to study the influence of dynamic effects that may dramatically affect

Design of Experiments in Metal Cutting Tests Coolant Coupling

313

Gundrill spindle head Gundrill

Chip Box

Workpiece

Dynamometer

Feed motion

Kistler signal analyzer

Charge amplifiers

Fig. 5.9. Schematic of the experimental setup.

Table 5.14. The levels of factors and their intervals of variation. Levels

x1 x2 x3 x4 (◦ ) (◦ ) (◦ ) (◦ )

+2 +1 0 −1 −2

34 30 25 22 18

24 22 18 15 12

20 17 14 11 8

16 14 12 10 8

x5 (mm)

x6 (mm)

x7 (mm)

x8 (mm)

x9 x10 x11 (◦ ) (m/min) (mm/rev)

1.50 0.75 0.00 −0.75 −1.50

1.50 0.75 0.00 −0.75 1.50

16.0 14.0 11.0 8.75 6.0

17.5 11.5 8.75 6.0 3.5

20 15 10 5 0

53.8 49.4 34.6 24.6 19.8

0.21 0.17 0.15 0.13 0.11

the experimental results. If a gundrill works under the condition where resonance phenomenon affects its performance, no DOE can be used because the response surface would not be smooth. Gundrills are intended to drill deep holes and thus their shanks can be of great length. As a result, the tool has a relatively low static and dynamic rigidity and stiffness. This, in turn, leads to the process being susceptible to dynamic disturbances, which results in vibrations. This is particularly true in the case considered, where the properties of the work material changes along the drill diameter presenting a combination of proeutectoid white cast iron (HB429-560) and grey pearlite cast iron (HB186-220). As known [24], these dynamic disturbances lead to the torsional and flexural vibrations of the shank.

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Table 5.15. Design matrix and experimental results. No.

R

x1

x2

x3

x4

x5

x6

x7

x8

x9

x10

x11

Tool life (min)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

56 88 87 32 44 94 78 42 4 41 54 65 3 11 48 43 40 66 15 77 8 16 25 61 33 24 27 52 85 19 81 47 26 9 97 5 49 7 45 21 70 84 30 53 2 12 1 31 89 34

+2 +2 +1 +2 0 +2 +2 0 −1 +2 −1 +2 0 0 +2 −1 +1 0 −1 −1 0 +2 +1 +2 +1 +1 +2 0 −1 +2 −1 0 +2 −1 +2 +2 −1 0 −1 +2 −1 +2 0 0 0 +1 +2 +2 +1 −1

−1 +1 +1 0 0 +1 −1 +1 −1 −2 −1 −1 +1 −1 −1 −2 +2 −1 0 −1 +2 −2 +1 −1 +1 −2 +1 +2 −2 −2 +2 −1 −2 +2 −2 +1 +2 −2 0 0 −2 +1 0 +1 −1 +1 −2 +1 0 −1

−1 −1 −2 −2 +1 +1 +2 0 +1 +2 +1 −2 0 +1 −2 0 +1 +2 −2 +2 +2 −1 −1 0 +2 +1 −1 +2 −1 +1 −2 −1 0 +2 +2 −1 0 +2 +2 0 0 −1 0 0 +1 −1 0 0 +1 +1

−1 +1 −2 +1 −1 +2 +1 −1 +2 +2 +2 +1 +2 +1 +1 0 +2 −2 +1 −1 −2 0 0 +1 −2 +2 −1 −2 +2 +2 +1 0 0 −1 +2 −1 −1 +1 −2 0 −1 −1 +1 0 +2 −1 0 −1 +2 +2

0 −2 −1 −2 0 +1 −2 +2 +1 0 +1 −2 +1 0 −2 +1 +1 −2 0 +1 −2 0 −1 0 −1 +1 0 +2 0 +2 −2 +1 +2 −1 0 0 +2 +2 −2 0 +1 0 −2 −1 −2 +1 0 −1 +2 −2

0 −1 −2 −1 0 +2 −1 +1 +2 0 +2 −1 +1 0 −1 +2 +2 −1 0 +1 −1 0 +2 0 +2 +2 0 −1 0 0 +2 −2 0 −2 −1 0 −2 0 +2 −1 −2 0 0 +1 −1 +1 −1 +2 0 +1

−1 −2 −2 −2 +1 −2 −2 −1 −2 −2 −2 −1 +1 −1 0 −2 −2 −2 −1 −1 0 +1 −1 −1 −2 −2 −1 −2 −1 0 −2 −2 −2 −1 −1 −1 −2 0 −1 −1 +2 −1 −1 −2 −1 0 +2 −2 −2 −1

0 +2 +1 +2 0 +1 +2 −1 +1 0 +1 +2 −2 0 +2 +1 +1 +2 0 −2 +2 0 −1 0 +1 +1 0 +2 0 0 +2 −2 +1 0 −1 0 +2 0 +2 +1 +2 0 0 0 +2 −2 −2 −1 +1 +1

−2 +1 −2 −1 +2 −1 0 −2 −2 +1 −2 0 +1 +1 0 −2 +2 −2 −2 −2 0 −2 +2 +1 +1 −1 −2 +2 +1 0 −2 +2 +1 −1 +1 −2 +2 0 +1 +1 +2 −2 −2 +1 −2 +1 +1 0 +2 −2

0 −1 +1 −1 −2 −2 −1 +1 −2 0 +1 −1 +1 −1 −1 −2 −1 0 −1 −2 0 +1 +1 0 −2 +1 0 0 0 −1 0 −1 0 −1 +1 0 −1 0 −1 −2 −1 0 −1 0 +1 0 −2 −1 0 +1

0 +2 −2 +2 +1 −1 −1 −2 −1 +1 −1 +2 0 +1 0 −1 −1 +2 +1 0 +2 +1 −2 +1 +2 −1 0 0 +1 −2 0 +1 −1 −2 0 0 −1 −2 0 +1 0 0 +2 −2 0 0 +2 −1 −1 0

260 215 170 251 300 273 220 123 167 160 116 208 79 348 173 207 157 185 368 77 157 193 400 200 166 187 210 143 187 168 112 97 138 253 135 251 233 122 258 230 60 270 401 390 140 126 103 420 173 93 continued

Design of Experiments in Metal Cutting Tests

315

Table 5.15. —Cont’d No. 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

R

x1

45 50 72 14 29 100 33 22 80 36 67 51 69 55 59 71 20 74 35 73 28 37 60 79 83 86 90 92 93 62 99 68

0 −1 +2 +2 +1 0 +2 −1 0 +1 0 +1 +1 0 0 +1 +1 +1 +1 0 +1 0 +1 −1 −2 +1 +2 −1 +1 +2 −1 0 +2 −1

x2 −1 −2 +1 −1 +1 −1 0 0 −2 0 0 +2 +1 0 0 +1 +1 +1 −2 +1 −1 +1 +1 +2 −1 0 +1 0 +1 +1 +2 −1 0 +2

x3 +2 0 −1 +2 −2 0 0 +1 −2 +1 −2 −1 −1 +1 0 −1 −1 −1 0 −1 −1 −1 −1 0 −2 0 −1 +1 −1 −1 −2 0 −2 0

x4 +1 +2 −1 +2 −2 0 0 +1 −2 +1 −2 −1 −1 +1 0 −1 −1 −1 0 −1 −1 −1 −1 0 −2 0 −1 +1 −1 −1 −2 0 −2 0

x5 +2 −1 0 −1 −2 +1 +2 −1 +2 −1 −1 0 +1 +2 0 +1 +1 +1 +1 +2 0 −1 0 0 −2 0 0 +2 +2 −2 −2 +2 +1 +1

x6 0 −2 +2 −2 −1 −1 0 −1 +2 −1 0 +1 0 +1 0 +1 +2 +1 +2 0 +2 +1 +2 +1 +1 +2 0 −1 0 0 −2 +1 +1 +1

x7 0 −1 −2 +1 −2 −2 0 −2 +2 −2 −2 −1 0 −2 0 −2 +1 −2 −2 −2 0 −2 −1 −2 0 +2 −1 +2 0 −1 −1 +2 −2 +1

x8 0 +1 −2 0 +2 +2 +1 +1 +1 +1 +2 −1 0 +2 0 +1 +1 +1 +1 0 −1 −1 −1 −2 +1 −2 0 +2 +1 0 0 −2 −2 −2

x9 +1 0 −1 +2 −1 −1 −2 0 −2 −2 +1 −2 +1 0 0 0 +1 0 −1 0 0 +1 −2 −1 −2 0 −2 −1 −2 +1 +1 0 0 0

x10 0 −1 0 −1 +1 +1 −1 −1 0 +1 +1 0 0 −1 0 −2 −1 −2 +1 0 +1 0 0 −2 +1 −2 0 +1 −1 −2 0 +1 0 0

x11 −2 −1 0 0 −2 −2 −1 −2 −1 −2 0 +1 +1 +2 0 −1 −1 −2 −1 −1 −1 −2 +1 +2 0 +2 0 +1 −1 +2 −1 0 +1 0

Tool life (min) 97 183 272 89 367 279 187 240 66 326 273 305 103 147 104 300 350 315 210 147 100 359 310 330 67 100 230 32 284 450 350 151 206 152

In order to characterize the dynamics of the gundrilling process, the cutting force and the amplitude of the shank vibration were measured and analyzed. For the case considered, the time of one tool revolution was tr = 0.19 s (the rotational frequency of the tool fr = 5 Hz, feed f = 0.15 mm/rev, cutting speed ν = 58 m/min), the frequency of shank flexural vibration was ffl = 320–350 Hz and its amplitude Afl = (38–46)×10−6 m, the frequency of shank torsion vibration ftr = 200–220 Hz in machining grey cast iron and ffl = 640–770 Hz, Afl = (2–4)×10−6 m, ftr = 300–320 Hz in machining proeutectoid white cast iron. The natural frequencies were fnx = 18.84Hz and fny = 23.32Hz (the first harmonic) for the shank of length lsh = 780×10−3 m having the ratio of maximum and minimum

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rigidities equal to 0.67 due to the V-flute made on the shank for chip removal. As shown, these natural frequencies do not coincide with those due to the shank vibrations, so there is no influence of the resonant phenomenon. This conclusion was corroborated using different cutting speeds and feeds. The same conclusion was made for torsional vibrations. As such, the critical angular velocity of the shank was calculated as  ωx2 ωy2 , ωcr = !  2 2 ωx +ωy2

(5.52)

where ωx,y = 2πfn(x,y) are angular natural frequencies of the shank with respect to the x and y axes, respectively. It was found that ωcr = 64.74 s−1 . Because the experimental points included in Table 5.15 are to be determined for the following range of the shank rotational frequency: ωm = 18.86–51.3 s−1 , it was concluded that there is no influence of torsional resonance on the test results. The following can be stated to summarize the results obtained. The frequency of chip formation causes forced vibrations of the drill. These vibrations are due to the high dynamic content of the cutting forces including the cutting torque. As such, the uncut chip thickness, represented by the cutting feed per revolution, plays an important role. The influence of this parameter on the axial force is shown in Fig. 5.10, and on the cutting torque is shown in Fig. 5.11. As follows from these figures, when the feed

Pa(kN) 2.4 f = 0.21mm/rev 2.2 0.17 mm/rev 2.0 0.15 mm/rev 1.8 0.13 mm/rev 1.6 0.11 mm/rev

1.4 1.2 0.2

0.4

0.6

0.8

1.0

1.2 n(m/s)

Fig. 5.10. Influence of uncut chip thickness (the cutting feed f ) on the axial force.

Design of Experiments in Metal Cutting Tests

MT (Nm)

317

n = 1.150 m/s 0.825 m/s 0.440 m/s

50

0.330 m/s

40

30 0.11

0.13

0.15

0.17

0.19 f(mm/rev)

Fig. 5.11. Influence of uncut chip thickness (the cutting feed f ) on the drilling torque.

changes from 0.11 to 0.21 mm/rev, the axial force increases by 50% at the same cutting speed. Increasing the cutting speed from 0.33 to 1.15 m/s leads to approximately a 20% increase in the axial force at the same feed. As was expected, the cutting torque has the opposite variations with the cutting speed and feed. The analysis of the records of the axial force (an example is shown in Fig. 5.12) and drilling torque allowed the following representation of these parameters Pa (t) = Pas +∆Pa (t)+δPa (t)

(5.53)

MT (t) = MTs +∆MT (t)+δMT (t),

(5.54)

where Pas and MTs are the static and time invariant parts of the axial force and drilling torque, respectively, ∆Pa (t) and ∆MT (t) are the time-dependent parts of the axial force and drilling torque due to the variation of the properties of the work material, respectively, δPa (t) and δMT (t) are the time-dependent parts of the axial force and drilling torque due to the cyclic nature of chip formation and interactions of the deformation and thermal waves. The experiments showed that the variation of the axial force ∆Pa (t) has the frequency proportional to the rotational frequency of the shank. Its amplitude increases with the feed and decreases with the cutting (rotational) speed. In the case considered, the variation of ∆Pa (t) was in the range from 11 to 19% of Pa . The variation ∆MT (t) of the drilling torque had smaller amplitude and was in the range from 10 to 15% of MT in the selected

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Tribology of Metal Cutting

dT ∆T

∆T

Axial Force Pa

∆Pa

∆Pa dPa

Pa

Time t Fig. 5.12. Structure of relationship Pa (t).

ranges of the feed and speed. The variation of the axial force δPa (t) was in the range from 13 to 24% and that of torque δMT (t) was in the range from 13 to 24% of Pa . The amplitude of δPa (t) does not vary under these given cutting conditions while that of ∆Pa (t) varies and its maximum corresponds to the beginning of period δT . Using these results, one may conclude that the resonance phenomenon in the tests conducted did not affect the drill performance significantly so that DOE can be used in the assigned ranges of feeds and speeds (Table 5.14). Model. Using the constructed matrix, the model determination was carried out using the simplified algorithm of GMDH [20,21], according to which the search for the model of the process under investigation is carried out among those accepted for the processes in the field considered. As discussed above, logarithmic models are normally used for tool life tests. As such, the domain of input factors was formed as ln x¯ . Because the function in Eq. (5.52) is unknown, the input domain was extended by introducing variables ln x¯ , (ln x¯ )−1 to the existing x¯ and (¯x)−1 . As such, the response was represented as ln y¯ . Each vector of the input factors in this domain includes nine (first in the order) geometrical parameters and two regime parameters and their set forms the domain of input variables ¯x, i.e. x¯ = x1 ,...,x11 

(5.55)

(¯x)−1 = x12 ,...,x22 

(5.56)

(ln x¯ ) = x23 ,...,x33 

(5.57)

(ln x¯ )−1 = x34 ,...,x44 

(5.58)

Design of Experiments in Metal Cutting Tests

319

As such, Eq. (5.52) can be re-written as

%
& ¯ E ln y¯ x = F x¯ ,(¯x)−1 ,ln x¯ ,(ln x¯ )−1 , B¯ + Θ,

(5.59)

%
&   where E ln y¯ x is the estimation of the response, F ¯x, B¯ is the unknown ¯ is the vector of the residual errors of the model. functional and Θ The basic GMDH algorithm (COMBI) uses an input data sample as a matrix containing N levels (points) of observations over a set of M variables. A data sample is divided into two parts. If regularity criterion AR(s) is used, then approximately two-thirds of the observations form the training subset NA , and the remaining part of observations (e.g. every third point with same variance) form the test subset NB . The training subset is used to derive estimates for the coefficients of the polynomial, and the test subset is used to select the structure of the optimal model, that is one for which the regularity criterion AR(s) assumes its minimum 1 # [yi − y¯ (B)]2 → min NB N

AR (s) =

(5.60)

1

Experience shows [20] that better results are achieved if the cross-validation criterion RRR(s) is used because it takes into account all the information available in the data set and it can be computed without recalculation of the system for each test point. Each point is taken successively as a test subset and then the mean of criteria is used 1# [yi − y¯ (B)]2 → min N N

RRR(s) =

NA = N −1,

NB = 1

(5.61)

1

To test a model for compliance with the differential balance criterion, the input data set is divided into two equal parts. According to this criterion, the selected model must yield the same results on both the subsets. The balance criterion yields the only optimal physical model solely if the input data are noisy. To obtain a smooth curve of criterion value, which would permit one to formulate the exhaustive-search termination rule, a full exhaustive search is performed on models classified into groups of equal complexity. The first layer uses the information contained in every column of the set so that the search is applied to partial descriptions of the form y = a0 +a1 xi ,

i = 1,...,M

(5.62)

Non-linear members are considered as new input variables in data sampling. The output variable is specified in this algorithm in advance by the experimentalist. For each model, a system of Gauss normal equations is solved. At the second layer all model candidates of the following form are sorted y = a0 +a1 xi +a2 xj ,

j = 1,...,M

(5.63)

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Tribology of Metal Cutting

Fig. 5.13. Combinatorial GMDH algorithm. 1 – data sampling; 2 – layers of partial descriptions complexion; 3 – form of partial descriptions; 4 – choice of best model sets for structure identification; 5 – additional optimal model definition by discriminating criterion.

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The models are evaluated for compliance with the criterion, and the procedure is carried out until the minimum of the criterion is found. To decrease the calculation time, it is recommended to select at a certain (6–8) layer a set of best F variables and to use them only in the further full sorting-out procedure. As such, the number of input variables can be significantly increased. For extended definition of the only optimal model, the discriminating criterion is recommended. Figure 5.13 represents the algorithm graphically. This algorithm can be implemented simply in the following way: an available Gauss procedure of a system of linear equations solution is set in a loop for the generation of all possible combination of inputs and evaluate the results on separate sub-sample (not used for learning) by error criterion. Then, the best model among the calculated is selected. The extended combinatorial GMDH algorithm can briefly be described as follows: 1. Input of parameters and data. 2. Preliminary data handling: norming, generation of secondary non-linear variables. 3. Selection of criterion: regularity, balance or cross-validation type and division of input data sample into learning subset and test subset. For the regularity criterion, it is proposed to range all the observations according to dispersion of function and take every third point to a test subset. 4. Three loops: – for each function, – for each number of variables (at each layer), – for all variable sets for a given variable number (a) selection of criterion, (b) estimation of coefficients on learning sample and criterion value on test subset. Coefficients are obtained by reducing the initial data array into quadratic array of normal equations, which are solved by the LSE (Least-Squares Estimation) (Gauss or Choletsky) procedure, (c) selection and saving of some best criterion values and corresponding ensemble of variable number for each layer, (d) end of the third loop. At the end of the second loop: (e) output of criterion value (as text or graph), (f) termination of procedure on user demand, (g) end of the second loop. At the end of the first loop: (h) output results: – regularization: selection of the best models by secondary criterion among the selected models,

322

Tribology of Metal Cutting – calculation of forecast value and errors, – output of several best models. (i) end of the first loop.

5. End. For the case considered, this algorithm allowed generating a model having RRR(s) = 14% after six rows of selection. At this stage, further complication of the model was found unnecessary, so only the estimates for the model’s coefficients were taken into consideration for further stages of selection. The model was obtained in the following form: y = b0 +b1 x5 x7 (x1 ln x3 )−1 −b2 x3 (x2 x6 )−1 −b3 x10 x11 (x1 )−1 −b4 x4 ln x6 (x7 )−1 −b5 x12 (x6 )−1 +b6 ln x6 (x5 x1 )−1

(5.64)

or transforming Eq. (5.64) into initial factors, one can obtain T = 6.7020−0.6518 +0.0168

ϕ2 α1 α2 ln c2 −0.0354 −0.0005 1 ϕ2 c2 md c2

ln c2 νf c2 md −2.8350 −0.5743 ϕ1 ϕ1 ln α1 ϕ1

(5.65)

The adequacy of the model was tested using procedure described in the Section, Adequacy of the Model. The mathematical model of tool life (Eq. (5.65)) indicates that tool life in gundrilling is a complex function of not only design and process variables but also of their interactions. The inclusion of these interactions in the model brings a new level of understanding about their influence on tool life. For example, it is known that the approach angle of the outer cutting edge (ϕ1 ) is considered as the most important parameter of the tool geometry in gundrilling because it has controlling influence on tool life and on other important output parameters [25]. Traditionally, this angle along with approach angle of the inner cutting edge (ϕ2 ) are selected depending on the properties of the work material. Although the contradictive influence of these angles has been observed [25], none of the studies reveals their correlations with the cutting regime as suggested by Eq. (5.65).

5.5.3 Optimization of the tool geometry Problems that involve the operation or the design of systems are generally of the type to which optimization principles can be beneficially applied. Unfortunately, there are no fundamental studies on the optimization of the tool geometry so that the tool geometry given by the tool manufacturer is considered as the best. Whenever one uses “best” or “optimal” to describe a technical system including the cutting tool, an immediate question to be asked is: “The best with respect to what criteria and subject to what limitations?” Given a specific measure of performance and a specific set of constraints, one can designate a system as optimal (with respect to the performance measure

Design of Experiments in Metal Cutting Tests

323

and constraints) if it performs as well as, if not better than, any other system which satisfies the given constraints. The term suboptimal is used to describe any system, which is not optimal (with respect to the given performance measure and constraints). The problem of optimization of the tool geometry can be thought of as: for a given cutting regime and process constraints, and for the selected performance measure(s) (tool life, production rate, cost per drilled hole, for example), find a combination of parameters of the cutting tool geometry that maximize (minimize when necessary) the chosen performance measure(s). In practical terms,  the problem is reduced to finding ¯ = F x, B¯ (given by Eq. (5.52)) which is a the extremum of the objective function A continuous function in the domain of its existence with respect to vector x¯ = (¯x1 ,..., x¯ 9 ). Such a problem can be classified as a multi-dimensional problem of optimization. A primary goal for the selection of an optimization method is to find a method which is adequate to the problem and its constraints and that, given good starting points, requires only a few iterations for finding a solution. The comparison of different optimization techniques showed that the Hook and Jeeves method [26] is the most suitable for the problem considered. The advantages of this method are: 1. the quality of solutions improves at each successive step on the response surface, 2. it is suitable for the response surface which may have deep narrow “cavities” – craters (thus the gradient methods are not suitable), and 3. self-acceleration. The essence of this method can be described as follows: first, the initial or starting point of vector x¯ = (¯x1 ,..., x¯ 9 ) is selected (¯x[0]). By changing the components of this vector, the vicinities of the starting point are investigated and, as a result, the direction ¯ is found. The climb (or descending) of increasing (decreasing) the objective function A ¯ increases (decreases). When there is no greater (smaller) value of A ¯ takes place until A in this direction, the step of climb (or descending) is reduced. If it does not help, this direction is abounded and a new search in the vicinity of the current point takes place. After few changes in the search direction, the method allows to reach the optimum point. A step of 3% of the initial value of each parameter involved in the study was used. The optimum parameters of the tool geometry corresponding to a tool life of 497 min, obtained using the Hook and Jeeves method, are: approach angle of the outer cutting edge (ϕ1 ) = 31.5◦ ; approach angle of the inner cutting edge (ϕ2 ) = 18.0◦ ; normal flank angle of the outer cutting edge (α1 ) = 14.5◦ ; normal flank angle of the outer cutting edge, α2 = 9.0◦ ; location distances c1 = 1.36mm, c2 = 0.9mm; location distance of the drill point md = 10.4mm for cutting speed ν = 0.43m/min and feed f = 0.11mm/rev.

References [1] Mason, R.L., Gunst, R.F., Hess, J.L., Statistical Design and Analysis of Experiments with Application to Engineering and Science, John Wiley & Sons, New York, 1989.

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[2] Montgomery, D.C., Design and Analysis of Experiments, John Wiley & Sons, New York, 2000. [3] Astakhov, V.P., Osman, M.O.M., Al-Ata, M., Statistical design of experiments in metal cutting. Part 1: Methodology, Journal of Testing and Evaluation, 25 (1997), 322–327. [4] Astakhov, V.P., Al-Ata, M., Osman, M.O.M., Statistical design of experiments in metal cutting. Part 2: Application, Journal of Testing and Evaluation, 25 (1997), 328–336. [5] Astakhov, V.P., Metal Cutting Mechanics, CRC Press, Boca Raton, USA, 1998. [6] Stephensen, D.A., Material characterization for metal-cutting force modeling, ASME Journal of Engineering Materials and Technology, 111 (1989), 210–219. [7] Plackett, R.L., Burman, J.P., The design of optimum multifactorial experiments, Biometrica, 33 (1946), 305–328. [8] Astakhov, V.P., An application of the random balance method in conjunction with the PlackettBurman screening design in metal cutting tests, Journal of Testing and Evaluation, 32 (2004), 32–39. [9] Bashkov, V.M., Katsev, P.G., Statistical Fundamental of Cutting Tool Tests (in Russian), Machinostroenie, Moscow, 1985. [10] Astakhov, V.P., Shvets, S.V., A novel approach to operating force evaluation in high strain rate metal-deforming technological processes, Journal of Materials Processing Technology, 117 (2001), 226–237. [11] Astakhov, V.P., A primer on gundrilling, F&M Magazine, (2002), 32–41. http://www. indmagdig.com/fmmag/article_archives.asp?action=details&article_id=416. [12] Astakhov, V.P., Gundrilling know how, Cutting Tool Engineering, 52 (2001), 34–38. [13] Astakhov, V.P., The mechanisms of bell mouth formation in gundrilling when the drill rotates and the workpiece is stationary. Part 1: The first stage of drill entrance, International Journal of Machine Tools and Manufacture, 42 (2002), 1135–1144. [14] Astakhov, V.P., The mechanisms of bell mouth formation in gundrilling when the drill rotates and the workpiece is stationary. Part 2: The second stage of drill entrance, International Journal of Machine Tools and Manufacture, 42 (2002), 145–152. [15] Astakhov, V.P., High-penetration rate gundrilling for the automotive industry: system outlook, SME Paper TPO4PUB249, 2004, pp. 1–20. [16] Holman, J.P., Experimental Methods for Engineers, McGraw-Hill, New York, 1994. [17] Swillinger, D., Kokoska, S., Standard Probability and Statistics Tables and Formulae, CRC Press, Boca Raton, USA, 1999. [18] Kronenberg, M., Machining Science and Application. Theory and Practice for Operation and Development of Machining Processes, Pergamon Press, Oxford, 1966. [19] Zorev, N.N., Metal Cutting Mechanics, Pergamon Press, Oxford, 1966. [20] Madala, H.R., Ivakhnenko, A.G., Inductive Learning Algorithms for Complex System Modeling, CRC Press, Boca Raton, USA, 1994. [21] Ivakhnenko, A.G., Polynomial theory of complex systems, IEEE Transactions on Systems, Man, and Cybernetics, 1(4) (1971), 364–378.

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[22] Ivakhnenko, A.G., Ivakhnenko, G.A., Problems of further development of the group method of data handling algorithms, Pattern Recognition and Image Analysis, 110 (2000), 187–194. [23] Ivakhnenko, A.G., Ivaknenko, G.A., The review of problems solvable by algorithms of the group method of data handling, Pattern Recognition and Image Analysis, 5 (1995), 527–535. [24] Sakuma, K., Taguchi, K., Katsuki, A., Self-guiding action of deep-hole-drilling tools, Annals of the CRIP, 30 (1981), 311–315. [25] Swinehart, H.J., ed. Gundrilling, Trepanning, and Deep Hole Machining, SME, Dearborn, MI, 1967. [26] Kelley, C.T., Iterative Methods for Optimization, The Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1999.

CHAPTER 6

Improvements of Tribological Conditions

Any modification of tribological conditions in metal cutting is considered as an improvement if it results in at least one of the following: • Improved tool life according to the criterion (or criteria when applicable) selected to evaluate this life for a given machining operation. • Improved productivity of a given operation by allowing higher cutting speed, feed or, sometimes, depth of cut. • Increased efficiency of a given operation (cost per drilled hole, for example). All methods of improvement of tribological conditions can be broadly divided into two categories: 1. Component methods. These methods include modification of component(s) of the cutting system prior to the cutting process to improve the tribological conditions. Although there are a great number of these methods, the following are common: 1.1 Cutting tool 1.1.1 Coating of the cutting tools with thin layer(s) of wear-resistant and/or friction-reducing (often referred to as tribological) materials [1–3]. 1.1.2 Polishing of the rake and flank surfaces of cutting inserts to reduce the roughness of these surfaces in order to prevent severe adhesion. 1.1.3 Improving microgeometry of the cutting wedge by special edgepreparation honing technology, which is particularly beneficial for tools with polycrystalline diamond (PCD) and Cubic boron nitride (CBN) tool materials [4]. 1.2 Workpiece 1.2.1 Altering the properties of the work material by introducing special heat treatment such as isothermal annealing. 326

Improvements of Tribological Conditions

327

1.2.2 Reducing the strain to fracture of the work material by adding sulfur, lead or combinations of both (the so-called free-machining steels) [5]. 1.2.3 Changing the mechanical and contact properties of the work material by changing its chemical composition, for example Fe–Si and Ca–deoxidized steels to enhance its machinability [5–7]. 2. Systemic methods. These are used when all the components of the cutting system are actually engaged in cutting, i.e. when the cutting system is in existence. Among them, the following are mostly used: 2.1 Application of various cutting media (often referred as cutting fluids or simply coolants). 2.2 Alternation properties of the layer being removed: (a) machining with plastic deformation of the layer being removed ahead of the cutting tool; (b) machining with preheating of the layer being removed (by laser beam, plasma, induction heating, etc.). 2.3 Introduction of specially directed forced vibrations (often ultrasonic) into the cutting process. These are applied to the tool or to the workpiece resulting in the reduction of the cutting force, better penetration of the cutting fluid at the tool–chip and tool–workpiece interfaces, and, sometimes, in better integrity of the machined surface [8]. This chapter aims to introduce the most vital and basic tribological aspects of the cutting fluid application as the most representative and widely used systemic and component (correspondingly) method for the improvement of tribological conditions in metal cutting. It also discusses some important aspects of coating applications and metallurgical structure of the work material.

6.1 Cutting Fluids (Coolants) 6.1.1 General The basic functions of a cutting fluid are to provide cooling and lubrication and thus reducing the severity of the contact processes at the cutting tool–chip and cutting tool– workpiece interfaces. As a result, a cutting fluid may significantly affect the tribological conditions at these interfaces by changing the contact temperature, normal and shear stresses and their distributions along the interfaces, type and/or mechanism of tool wear, machined surface integrity and machining residual stresses induced in the machined parts, etc. In some applications, it is expected that a cutting fluid should also provide secondary service actions as, for example, washing of the machined part; chip transportations as in deep-hole drilling where a cutting fluid transports the chip over significant distances. Historically, until nineteenth century, water was used as a cooling medium to assist various metalworking operations. Taylor [9] was probably the first to prove the practical value of using liquids to aid in metal cutting. In 1883, he demonstrated that a heavy stream

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of water flooding the cutting zone increased the allowable cutting speed by 30–40%. It was found, however, that although water is an excellent coolant due to its high thermal capacity and availability [10], corrosion of parts and machines and poor lubrication were the drawbacks of such a coolant. Further developments followed quickly. Mineral oils were developed at this time as these have much higher lubricity, but the lower cooling ability and high costs restricted this use to low cutting speed machining operations. Finally, between 1910 and 1920 soluble oils were initially developed to improve the cooling properties and fire resistance of straight oils [10]. Other substances are also added to these to control problems such as foaming, bacteria and fungi. Oils as lubricants for machining were also developed by adding extreme pressure (EP) additives. Today, these two types of cutting fluids (coolants) are known as water emulsifiable oils and straight cutting oils. Additionally, semi-synthetic and synthetic cutting fluids were also developed to improve the performance of many machining operations [11]. Although the significance of cutting fluids in machining is widely recognized, cooling lubricants are often regarded as supporting media that are necessary but not important. In many cases, the design or selection of the cutting fluid supply system is based on the assumption that greater the amount of lubricant used, the better the support for the cutting process. As a result, the contact zone between the workpiece and the tool is often flooded by the cutting fluid without taking into account the requirements of a specific process. Moreover, the selection of the type of the cutting fluid for a particular machining operation is often based upon recommendations of sales representatives of cutting fluid suppliers without clearly understanding the nature of this operation and the clear objectives of cutting fluid application. The brochures and websites of cutting fluid suppliers are of little help in such a selection. The techniques of cutting fluid application, which includes the cutting fluid pressure, flow rate, nozzles’ design and location with respect to the machining zone, filtration, temperature, etc., are often left to the discretion of machine and tool designers. Moreover, the machine operators of manual and semiautomatic machines are often those who decide the point of application and flow rate of the cutting fluid for each particular cutting operation. The cutting fluids also represent a significant part of the manufacturing costs. Just two decades ago, cutting fluids accounted for less than 3% of the cost of most machining processes. These fluids were so cheap that few machine shops gave them much thought. Times have changed and today cutting fluids account for up to 15% of a shop production cost [12]. Figure 6.1 illustrates the cost of production of camshafts in the European automotive industry [13,14]. The conspicuous high share of the costs for cooling lubrication technology reaches 16.9% of the total manufacturing costs. As directly follows from Fig. 6.1, the costs of purchase, care and disposal of cutting fluids are more than 2-fold higher than the tool-related costs, although the main attention of researchers, engineers and managers is focused on improving the cutting tools. Moreover, cutting fluids, especially those containing oil, have become a huge liability. Not only does the Environmental Protection Agency (EPA) regulates the disposal of such mixtures, but many states and localities also have classified them as hazardous wastes. At present, many efforts are being undertaken to develop advanced machining processes using less or no coolants [15–17]. Machining without the use of cutting fluids has become a popular avenue for eliminating the problems associated with the cutting fluid

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Structure of Manufacturing Costs Tool costs 7.5%

Machine tool costs 38.3%

Staff costs 8.8%

General costs 27.5%

Costs of coolant application 16.9%

(a)

Structure of Manufacturing Costs Depreciation and waste disposal 59%

Cleaning 3.7% Service 10.7%

Laboratory equipment 5.2% Electricity 2.9%

Staff 14.3%

(b) Fig. 6.1. Pie-chart representations of: (a) manufacturing cost at the German automotive industry and (b) structure of coolant cost.

management [18]. One of the greatest obstacles to the acceptance of dry machining is the false belief that cutting fluids are needed to produce high-quality finish, although a number of studies have shown otherwise. As anything in this world, dry machining has its advantages and associated drawbacks. The advantages of dry machining are self-obvious: cleaner parts, no waste generation, reduced cost of machining, reduced cost of chip recycling (no residual oil), etc.

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These advantages do have a cost. The most prohibitive part of switching to dry machining is a large capital expenditure required to start a dry machining operation. Machines and tools designed for cutting fluids cannot be adapted readily for dry cutting [18]. New, more powerful machines must be purchased, and special tooling is often needed to withstand high temperatures generated in dry cutting. The quality of machined parts may be affected significantly as the properties of the machined surface are significantly altered by dry machining in terms of its metallurgical properties and machining residual stresses. High cutting forces and temperatures in dry machining may cause the distortion of parts during machining. Moreover, parts are often rather hot after dry machining so its handling, inspection gaging, etc., may present a number of problems. Promising alternatives to conventional flood coolant applications are also Minimum Quantity Lubricant (MQL) or Near Dry Machining (NDM) or Semi-Dry Machining (SDM). As the name implies, MQL uses a very small quantity of lubricant delivered precisely to the cutting zone. Often the quantity used is so small that no lubricant is recovered from the parts. Any remaining lubricant may form a film that protects the parts from oxidation or the lubricant may vaporize completely due to high temperatures of the cutting zone. It was pointed out, however, that the use of MQL will only be acceptable if the main tasks of the cutting fluid [19] (heat removal – cooling; heat and wear reduction – lubrication; chip removal; corrosion protection) in the cutting process are successfully replaced [20]. To make such a replacement, the understanding of the metal cutting tribology is vital.

6.1.2 Understanding the background of cutting fluids selection: what seems to be the problem? Although a great body of research and application data are available, actual action of cutting fluids is still an open issue in metal cutting. When cutting fluids are applied, the existence of high contact pressure between chip and tool rake face, particularly along the plastic part of the tool–chip contact length, should apparently preclude any fluid access to the rake face. In spite of this self-obvious fact, the theory considering these fluids as boundary lubricants is still leading [21] and thus explaining the marked influence which cutting fluids have on the cutting process outputs (cutting force and temperature, surface finish and machining residual stresses, tool wear). Unfortunately, these outputs have never been analyzed systematically to correlate them with the parameters (type, make, brand, flow rate, pressure, application technique, etc.) of the cutting fluid used. The known books and publications on cutting fluids, and their selection and application techniques are of little help in the intelligent (purposive or goal-directed) selection of the parameters of the cutting fluid. Although these books and multiple published articles describe in detail the chemical and physical (thermal, rheological, etc.) properties of various cutting fluids and their components, they provide only qualitative descriptions of correlation of these properties with metal cutting conditions using very vague words as “improve,” “increase,” etc. No quantitative data are provided because these are simply unavailable. Even when a serious team of applications specialists in the automotive industry tries to deal with the issue and thus attempt to develop a kind of standards for cutting fluids (for example GM LS2 [22]), the maintenance issues associated with the cutting fluid overshadow the cutting actions and tests of these fluids.

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In the author’s opinion, the lack of elementary knowledge on metal machining tribology prevents intelligent decision-making in the whole cutting fluid business. As a result, in the automotive industry, the associated costs often overshadow those savings gained due to implementation of advanced cutting tools, tool materials, coating etc. Because the cutting tool and cutting fluid businesses are normally outsourced to different commodity management companies, the automotive companies cannot see this obvious fact.

6.1.3 Application aspect of the selection and implementation of the cutting fluids Selection of the coolant chemistry (composition, make etc.). As pointed out by Childers [10], the chemistry of metalworking fluids is as diverse as a library of cookbooks. Each formulating chemist working in a small local or big international metalworking fluid company develops his own fluid formula to meet the performance criteria of the metalworking operations or a group of similar (in his opinion) operations. But like “lasagna,” each “recipe” has common ingredients or raw materials: pasta noodles, cheese(s), souse, meat, Italian seasoning, etc. That is why metalworking fluids are at times called “black box chemical blends.” No user is fully aware of the exact composition of the fluid used, but the user knows whether it meets certain performance criteria (tastes good). There are many additives and blends that may function as metalworking fluids and there is no assurance of the “perfect” fluid for an operation. Misapplication of that perfect fluid could render unacceptable. Trying out a coolant on a machine. According to Metalworking Fluids Magazine [23], you cannot intelligently select the best metalworking fluid by “trying it out on a machine” because there are many variables between fluids, machines and operations and you will be wasting time and money. You are not likely to learn anything, and anything you do learn will apply to that machine alone. Worse, you have established precedence on a procedure that does not work. Therefore, proper laboratory testing should always precede field test. Get help in the selection and application of the “perfect” cutting fluid from “professionals.” According to Metalworking Fluids Magazine [23], if you ask for assistance from a cutting fluid salesperson, he will suggest the perfect cutting fluid and offer to watch this cutting fluid during the test period. Unfortunately, experience shows that this is not the best way to go with because even if a good result is achieved, it does not last so you wait for another salesman to come and ask you “try another one out on this other machine.” Laboratory testing of the cutting fluid. As pointed out by Byers [24], manufacturers spend hundreds of thousands of dollars on the machines, tens of thousands of dollars on the skilled operator, hundreds or thousands of dollars on the cutting tool or grinding wheel, and only pennies per mix gallon on the metalworking fluid. Yet, if the fluid is not correctly selected and/or its application techniques are not suitable for the operation, the results are scrap and/or poor-quality parts and thus the entire investment will be wasted. Therefore, the result of laboratory testing seem to be very helpful in the selection of the application-specific cutting fluid. Reality, however, is much less bright and promising.

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Although Byers [24] pointed out that a laboratory test must be meaningful presuming the most important conditions of the metalworking operation, the problem is that these conditions (which are actually the tribological conditions) are not clearly understood or known. As a result, many properties measured in laboratory testing, for example specific gravity, viscosity, flash and fire points, neutralization number, stability determinations (neat product stability and dilution stability), foam tests, oil rejection, pH measurements, alkalinity, emulsifier content, boron content, microbicide level, etc., relate to the cutting fluid maintenance rather than to the tribological characteristic of the metal cutting system. The most important performance characteristics presumably related to metal cutting tribology is called lubricity. The types of lubricity test of metal cutting fluids known today can be broadly divided into two groups. The first group is most common and is based on simple rubbing action. The second group includes actual metal cutting under controlled conditions. Rubbing tests. Byers [24] admitted that because of the complexity of field conditions, no single test machine can simulate the lubrication requirements for all in plant manufacturing operations. He suggested that different lubricity tests should be used to evaluate metalworking fluids. He did not point out, however, how many tests should be used. Moreover, there is no indication how to compare and compile the test results to arrive at any meaningful conclusion about the particular properties of the cutting fluid as related to the actual cutting operation. The Falex Pin and Vee method (ASTM D2625-94(2003)) is the most widely used, and, yet of least value with respect to metal cutting and grinding. A standard Pin and Vee tester can measure two qualities of a lubricant, namely its lubricity and the maximum pressure it withstands before the lubricating properties fail. Tests can be performed at various temperatures. It operates by having a small, rotating, cylindrical pin squeezed between two metal arms with vee-notched blocks attached, as shown in Fig. 6.2. The testing can be performed by immersion in oil which is being heated to a desired temperature. It is also suitable for testing dry film bonded lubricants and additive packages. Testing is performed to the following standards: • Endurance (Wear) Life and Load-Carrying Capacity of Solid Film Lubricants (Falex Pin and Vee Method) ASTM D-2625. • Measuring Wear Properties of Fluid Lubricants (Falex Pin and Vee Block Method) ASTM D-2670. • Measurement of Extreme Pressure Properties of Fluid Lubricants (Falex Pin and Vee Block Methods) ASTM D-3233. The Four Ball Wear Test (ASTM D-4172) determines the wear protection properties of a lubricant. Three metal balls are clamped together and covered with the test lubricant, while a rotating fourth ball is pressed against them in sliding contact (Fig. 6.3). This contact typically produces a wear scar, which is measured and recorded. The smaller the average wear scar, the better the wear protection provided by the lubricant.

Improvements of Tribological Conditions

Revolving journal V blocks

Fig. 6.2. Pin and Vee-block lubricity test.

Fig. 6.3. Four-ball lubricity test.

333

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There are a number of other tests as, for example, the block-on-ring and pin-on-ring Falex-type lubricity tests that can be used to evaluate lubricity of the cutting fluid. Although these tests are widely used to evaluate the performance of cutting fluids, one should clearly realize that it is difficult, if not impossible, to correlate bench test data with actual performance of the cutting fluid. This is because a number of crucial differences exists between the test conditions in rubbing tests and actual metal cutting: • The major problem is that in rubbing tests, the continuous sliding contact occurs by cyclic reintroduction of the same surface element from the counter-material. Although repeated contact occurs between many machine elements, such as journal bearings, rotating seals and engine pistons, in metal cutting, by contrast, tools generally slide against a freshly formed, not previously encountered surface. The physics and chemistry of this freshly formed surface (referred to as the juvenile surface) are considerably different from the contact surface in rubbing test. • To prove this point conclusively, Zorev [25] carried out cutting tests using mercury as the cutting fluid. Normally, mercury as a cutting fluid would not pass ASTM standard tests because it would not wet the steel surface. In metal cutting, however, it is absorbed very easily by the chip’s freshly formed surface covering it with a thin layer of amalgam. This thin layer of amalgam offers a low shear resistance and sharply reduces friction at the tool–chip interface that results in a significant reduction of the cutting forces and improvement in tool life. In cutting low carbon steel, a 40% reduction in the cutting force and a 30% improvement in tool life have been obtained. Similar results were obtained with other “non-traditional” cutting fluids as, for example, liquid oxygen. • Metal cutting is the process of formation of new surfaces. As such, as conclusively proven by Atkins [26], great values of surface-specific work are involved. There is no such work found in rubbing tests. • Tribological conditions in rubbing test do not even remotely resemble those found in metal cutting. In other words, the level and distribution of the normal and shear stresses along the contact interfaces as well as the temperature and its distribution over these interfaces are principally different in these two processes. Due to these differences, the physical processes occurring at the rubbing test and metal cutting interfaces are highly dissimilar. Actual metal cutting under controlled conditions. One of the most popular tests in recent years is the Tapping Torque test [24] conducted using the guidelines of ASTM D 5619 standard. The Falex Tapping Torque Test Machine is normally used to evaluate metalworking fluids and tools. The machine uses a high-precision tap and a wide range of reproducible nut blanks in cutting or forming operations. This machine provides data for the evaluation of cutting oils, tool life, tap design and machinability of metals. The determination of cutting efficiency is based on an accurate and fast measurement of the cutting torque, exerted on nut blanks. ASTM D 5619 standard considers this method as the only acceptable method of data evaluation while methods based on power consumption by the driving motor are not considered to be accurate. The average of any segment

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of a torque curve may be studied using a computer data acquisition system. A recent improvement has been realized at Falex: utilization of a 9.5 mm cutting tap instead of a 10 mm tap. The smaller tap allows better circulation of fluid and exit of chips during operation. In most cases, its use has provided better repeatability and differentiation. The Tapping Torque test is used to evaluate the efficiency of cutting fluids. Several fluids may be compared. One of the cutting fluids under the test is defined as the reference fluid (100% efficiency) and all other fluids are rated against this reference. However, tool wear causes gradually increasing tapping torque. A reference line is established by running the reference fluid between the other fluids. The torques measured with other cutting fluids under testing will either fall above (more torque required, therefore less efficient) or below (more efficient) this line. The repeatability of the obtained results is then verified using additional tests, where the reference cutting fluid and one or two cutting fluids which showed the best results at the first stage are tested separately. There are a number of other non-standardized evaluation tests used today as the drilling test, the turning test, etc. Apart from many other problems, the most common problem with these tests is a great number of test variables involved including a significant variation in the performance of tools from the same lot. As a result, one may wonder what is actually tested: variation of the tool manufacturing quality or cutting fluid properties. This is well summarized by Russell [27] who pointed out that “there are definite performance variables that exist between manufacturing lots (of twist drills), as well as variables in tool performance of the same lot.” Although the actual metal cutting tests seem to be the best way to study the performance of the cutting fluid, there are a number of reservations about the results of such a test because: • To obtain meaningful results, the laboratory and field conditions must be exactly same or similar. Unfortunately, this similarity is evaluated by eye rather than using similarity theory. Because ASTM did not adopt (at least that far) any standard procedure for human eye evaluation and certification, such evaluation cannot be considered to be an objective. • Condition of machining system may affect the results dramatically. Even small machine tool misalignment (caused by a number of reasons: tool holder accuracy, spindle runout, part-holding inaccuracy, etc.) may completely discard any differences in the performance of various cutting fluids. • The results obtained using the standardized Tap Test can hardly be extended over the whole range of metal machining operation (boring, milling, drilling, turning, etc.) where the tribological conditions can significantly differ from those in the Tap Test. For example, the cutting speed differs 20–30-fold, contact pressure – more than 10-fold, cutting temperature – 3–5-fold, etc. All these results in different tribological processes and wear mechanisms involved. For example, diffusion wear of the cutting tool is quite common in high-speed machining while it cannot occur (physically) in the Tap Test.

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6.1.4 Cutting theory aspect of selection and implementation of the cutting fluids A great number of hypotheses on the influence of various cutting fluids on the metal cutting process have been advanced over the last 100 years. They have, however, not progressed enough to understand what is really happening at the contact interfaces when the cutting fluid is applied. Although many experimental studies have been carried out to verify these hypotheses, no clear picture of the functioning of the cutting fluid is emerged that far. No conclusive results have been obtained to support the development and implementation of efficient cutting fluids. Among the open issues, the following are outstanding: (1) the way in which cutting fluids can penetrate into the contact interfaces; (2) action(s) of the cutting fluid, i.e. whether cutting fluids are coolants or lubricants or both and if so, to what extent these effects overlap or predominate. Penetration of the cutting fluid into the contact interfaces. To account for cutting fluid penetration into the contact interfaces (on the rake and flank faces), four basic mechanisms of cutting fluid access have been suggested, namely, access through capillarity network between the chip and tool, access through voids connected with built-up edge formation, access into the gap created by tool vibration and propagation from the chip blackface (free surface) through distorted lattice structure. However, no conclusive experimental evidences are available to support any of these suggestions. According to known literature sources [25,28,29], capillarity may play a significant role. According to these sources, the microscopic valleys and hills on the chip and cutting tool contact surfaces form a network of fine capillaries permitting the pressure gradient between the outside media and vacuum in the capillaries to facilitate cutting fluid penetration. Williams and Tabor [28] even calculated this pressure gradient showing that the reduction in the friction force on the tool rake face might be as much as 75% due to cutting fluid penetration although no conclusive experimental evidence have been presented. Unfortunately, the considerations of cutting fluid penetration due to capillarity network between the chip and tool cannot pass a simple reality check because: • The highest specific pressures known in engineering occur in metal cutting at the interfaces [30] so the chip contact layer, brought to very plastic state, fills all the microscopic valleys at the tool–chip interface. This pressure is much higher than that in pressure sealing metal gaskets for 17 MPa flange rating where no leaks due to capillarity occur. Unfortunately, the lack of tribological understanding of metal cutting did not allow the researchers to compare the pressure at the tool–chip interface (discussed in Chapter 3) with the so-called sealing pressure under which no cutting fluid penetration is possible even theoretically. • High contact temperatures at the tool–chip and tool–workpiece interfaces would cause evaporations of any cutting fluid at a far distance from the highest temperature and contact pressure zones.

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Other suggested ways of cutting tool penetration are even more illusive. Access through voids connected with built-up edge is not very likely because the built-up edge does not exist at the range of cutting speeds used today. Access into the gap created by tool vibration is not likely because the amplitude of vibration is extremely small so the chip does not disengage with the tool [31]. Propagation from the chip blackface through distorted lattice structure cannot happen physically due to extremely short time of chip deformation [32]. In the author’s opinion, the most conclusive results were obtained by a research team headed by Talantov [33]. This study can be summarized as follows. Low-, medium- and high-carbon steels were selected as work materials. A special setup where the dropping cutter with separable cutting inserts was installed in a specially designed pendulum-type device. The cutting insert was allowed to disengage “to freeze” the cutting insert – partially formed chip at different cutting conditions. After the test, a “frozen” part containing the partially formed chip in its contact with the cutting insert was cutoff from the rest of the workpiece for further studies. A scanning electron microscope was used to investigate the geometry of the tool–chip contact at 6000–10 000× magnification. Using an X-ray microanalyzer, the nature of the tool–chip contact was studied. The test results proved that there are two distinctive regions within tool–chip contact, as discussed in Chapter 3. The material of the chip was found to fill out even the microscopic valleys and hills on the cutting insert contact surface at a level below the surface roughness, and so no network of fine capillaries was found. Moreover, the zone of plastic contact was observed at the tool–chip and tool–workpiece interfaces. The evidence of intensive diffusion was found within this zone that completely excludes even the finest capillaries. To study the possibility of cutting fluid penetration at contact surfaces objectively, a series of tests were carried out in which the various cutting fluids with added radioisotope T-3 (tritium H3) were used. Test conditions were as follows: work material – AISI steel 1045; tool material – standard carbide M10; tool geometry – normal rake angle 0◦ , normal flank angle 10◦ , cutting edge angle 45◦ , cutting edge inclination angle 0◦ ; cutting speed range 30–140 m/min; feed range 0.12–0.45 mm/rev; depth of cut 2 mm. The tests included 5 min of cutting at intensive cutting regimes and quick process interruption with a specially designed quick-stop device. Then, the tool contact surfaces were examined using radiography. The results of this experiment showed no traces of radioisotopes at the plastic part of the tool–chip and tool–workpiece interfaces. Small traces of radioisotopes within the elastic part of the tool–chip and tool–workpiece interfaces were found only on very few test specimens. The major result of this research program conclusively proves that the cutting fluid does not penetrate the contact surfaces at the discussed interfaces. All the known “look-nice stories” about EP additives (chlorine, sulfur and fatty acids for example) that, according to literature sources, are added to the cutting fluid to prevent severity of the chip and workpiece contacts where the chip has no ground. On the other hand, their use in metal

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cutting has proven to be successful in terms of improving the tool life, reducing the cutting forces and improving the integrity of machined surfaces. Therefore, another mechanism of their action should be suggested and verified if one tries to improve the tribological conditions in metal cutting by using the cutting fluids. Cooling action. In terms of metal cutting tribology, the commonly referred actions of the cutting fluid are the lubrication and cooling. Being self-obvious, the former is most widely tested using various standards (above discussed) and tailored tests while the latter did not attract much attention besides the general perception that water-soluble cutting fluids possess higher cooling ability than waterless ones. Unfortunately, there are no characteristics of the cooling action of cutting fluid is readily available at tool and process designers’ disposal although a number of studies are known (for example [34,35]). Moreover, in the author’s opinion, the most important action of cutting fluid is the embrittlement action which did not attract much attention in the literature on metal cutting and cutting fluids. As pointed out in the literature on metal cutting, most of the mechanical energy associated with chip formation converts into the thermal energy [30,36]. For example, Epifanov and Rebinder [38] conducted a series of tests using a specially designed setup to study the energy balance in metal cutting. The setup included a calorimeter and a dynamometer so the thermal energy generated in cutting was measured directly while the mechanical energy spent in cutting was calculated as a product of the measured cutting force and the cutting speed. Wide ranges of work materials and cutting regimes were used in the study. The results of this study conclusively proved that 99% of the energy is spent in cutting converts into the thermal energy while in standard metrical testing (tensile, compression, impact) such a conversion was found to be in the range of 0.75–0.93%. Because practically all the mechanical energy associated with chip formation converts into the thermal energy, the heat balance equation is of prime concern in metal cutting studies [32]. Accounting for the energy flows in the cutting system, discussed in Section 6.2.2, this equation can be written as Pc = Fz ν = QΣ = Qch + Qw + Qct ,

(6.1)

where Pc is the cutting power, Fz is the power component of the cutting force, ν is the cutting speed, QΣ is the total thermal energy generated in the cutting process, Qch is the thermal energy transported by the chip, Qw is the thermal energy conducted into the workpiece and Qct is the thermal energy conducted into the tool. Table 6.1 presents the result of energy balance study in metal cutting [32] in machining steel 1045 using experimentally obtained chip compression ratios. As seen in these experiments, most of the thermal energy generated in the cutting process is carried away by the moving chip. At cutting speeds used today, this portion has reached 80–85%. Approximately, equal portions of the total thermal energy generated in cutting are conducted into the workpiece and into the tool. As follows from the data presented in Table 6.1, the ratio of these portions varies significantly with the cutting speed. As the speed increases, greater portion of the thermal energy is conducted into the tool.

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Table 6.1. Energy balance in machining (steel 1045). ν (m/s) 0.10 0.20 0.50 1.00 2.00 4.00

Pe 1.76 3.52 8.80 17.60 35.20 70.40

Qch (J/s) Qch /QΣ Qw (J/s) Qw /QΣ Qct (J/s) Qct /QΣ QΣ (J/s) (%) (%) (%) 47.9 93.7 272.3 501.6 1177.1 2306.2

50.2 55.7 70.3 76.2 82.8 86.3

38.4 63.7 100.3 136.9 217.5 336.7

40.2 37.8 25.9 20.8 15.3 12.6

9.2 11.0 14.7 19.7 27.0 29.4

9.6 66.6 3.8 3.0 1.0 1.1

95.5 168.4 287.3 658.3 1421.6 2572.3

Although most of the thermal energy generated in the cutting process is carried away by the moving chip, it must, however, not be concluded that the chip temperature is higher than the tool temperature. In reality, it is much lower. This is simply because the chip moves and thus mass transfer takes place so that any elementary volume of the moving chip is not exposed to high contact temperatures for sufficient time to increase the chip temperature significantly. The same can be said about the workpiece as the tool moves over its surface, “spreading” the generated thermal energy over all machined surface. On the contrary, the tool contact surfaces at the tool–chip and tool–workpiece interfaces do not move. As a result, the tool contact temperatures are normally much higher than those of the chip and the workpiece. The matter worsens because new superhard tool materials (CBN, cermets, ceramics, etc.) have very low thermal conductivity, so the tool cannot dissipate the thermal energy generated at the interfaces fast enough, which results in extremely high temperatures at the tool contact surfaces. The observations of the cooling action of a cutting fluid allow the following conclusions: • Slightly reduces the cutting temperature at cutting speeds up to 150 m/min. At higher cutting speed, it just stabilizes the temperature of the workpiece. As discussed in Chapter 4, there is an optimal cutting temperature that correlates the minimum tool wear. Therefore, the cooling action of a cutting fluid is helpful in terms of tool life if it brings the cutting temperature closer to the optimal cutting temperature. Otherwise, tool life is not improved but rather reduced in many conventional machining operations as found by Seah et al. [18]. Unfortunately, this important issue has never been explained and thus addressed in the published materials on cutting fluids. Although the reduction of the cutting temperature due to the cooling action of the cutting fluid appears to be small [39] and thus it might appear that the cutting fluid has little effect on the tool–chip interface tribological process. In reality, however, it is not quite true. Experiments showed that if the cutting temperature exceeds the optimal temperature at the tool–chip interface and diffusion wear takes place there, a 10–15% decrease in the contact temperature leads to a 2–3-fold reduction in the coefficient of diffusion between the tool and the work materials. • Improves accuracy of machining. By reducing the temperature of the tool and workpiece, better accuracy of machining can be achieved as a result of reduced temperature deformation of the components of the machining system.

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• Reduces the radius of curvature of the chip. The lower the thermal conductivity of the work materials, the greater the reduction. This aspect should be accounted for in the design of obstruction-type chip breakers, where this radius is an important design consideration. • Reduces the tool–chip contact length. This is a negative aspect because the cutting forces are not normally reduced. As a result, higher contact stresses act at the tool– chip interface that may result in a lower tool life. This is particularly important for brittle tool materials, which may experience the chipping of the cutting edge. • Increases thermal shock in interrupted cuts. For example, such as those occuring in milling can cause thermal cracking on the cutting wedge. Once started, the crack will grow causing either a catastrophic failure of the cutting insert or a loss of dimensional accuracy and surface finish on the parts. Direct cooling action. The cooling action of the cutting fluid is due to forced convection. As such the heat transfer is given by   Q = Acl hcv θsf − θcf , (6.2) where Acl is the heat transfer area of surface, hcv is the convection heat transfer coefficient of the process, θcf and θcf are the temperatures of the surface and cutting fluid, respectively. Although convective heat transfer problems can seem incredibly confusing given the multitude of different equations available for different systems and flow regimes, one should keep in mind that the whole goal of the problem is to find the overall heat transfer coefficient, hcv so the problem of heat transfer from the object in the fluid medium can be solved using Eq. (6.2). Because this coefficient depends on many physical and design parameters, its determination requires introduction of some similarity numbers as: The Reynolds Number (Re) Re =

νcf beq , νcf

(6.3)

where νcf is the velocity of the cutting fluid, beq is the equivalent length (diameter or other length-scale) and νcf is the kinematic viscosity of the cutting fluid. For forced convection problems Re determines whether or not the flow is turbulent or laminar. For flow past flat plates, the transition region from laminar to turbulent is about 105 < Re < 107 . The Nusselt Number (Nu) Nu =

hcv beq , kcf

where kcf is the thermal conductivity of the cutting fluid.

(6.4)

Improvements of Tribological Conditions

341

The Nusselt Number is defined as the ratio of convection heat transfer to fluid conduction heat transfer under the same conditions. The Prandtl number (Pr) characterizes thermal properties of the cutting fluid Pr =

νcf , αcf

(6.5)

where αcf is the thermal diffusivity of the cutting fluid. It is related to the following characteristics of the cutting fluid: thermal conductivity kcf , specific heat CP−cf , density ρcf by αcf =

kcf ρcf CP−cf

(6.6)

To describe heat transfer, the following generic relationship is used Nu = cfc Ren Pr m ,

(6.7)

where cfc is a constant. The particular values of cfc , n and m depend on the relative location, the cutting fluid flow and the cooled surface [40,41]. The most general case is the interaction of the cutting fluid flow with a flat surface set perpendicular to this flow. In this particular case Nu = 0.20Re0.65 Pr 0.33

(6.8)

or substituting Eqs. (6.3)–(6.6) into Eq. (6.8), recalling that ρcf = γcf /g, and expressing hfc , one can obtain hfc =

0.65 k 0.67 (C 0.33 νcf P−cf γcf ) 0.20 cf × , 0.32 b0.35 g0.33 νcf

(6.9)

where γcf is the specific weight of the cutting fluid and g is the acceleration due to gravity. Although Eq. (6.9) has a clear structure and thus can be analyzed directly, much more general results can be obtained if one realizes that its first term is an application-specific constant. Therefore, we can introduce a new parameter called the cooling intensity Kh which includes only the second cooling-process-specific term of Eq. (6.9), 0.65 0.67 0.33 0.33 −0.32 Kh = νcf kcf CP−cf γcf νcf

(6.10)

As seen, the velocity of the cutting fluid νcf affects its cooling ability almost as much as its thermal conductivity kcf and much more than its specific heat CP−cf . Table 6.2 shows

Water – normal application (flooding from the chip free surface at νcf = 0.2 m/s and temperature θcf = 20◦ C) Soluble oil of 10% concentration – normal application Kerosene – normal application Carbon tetrachloride (CCl4 ) – normal application Pure gear box oil – normal application Cutting strait oil with chlorine and sulfur – normal application Compressed air at velocity 100 m/s and temperature θcf = 20◦ C Compressed air at velocity 100 m/s and temperature θcf = −40◦ C Compressed air at velocity 300 m/s and temperature θcf = 20◦ C Compressed air at velocity 300 m/s and temperature θcf = −40◦ C Compressed air at velocity 500 m/s and temperature θcf = 20◦ C Compressed air at velocity 500 m/s and temperature θcf = −40◦ C

Cutting fluid

0.999 0.884 0.448 0.127 0.436 0.240 0.240 0.242 0.240 0.242 0.240 0.242

0.297 0.126 0.087 0.109 0.103 0.0223 0.0182 0.0223 0.0182 0.0223 0.0182

kcal kg·◦ C

Specific heat (CP−cf )

0.515

kcal m·h·◦ C

Thermal conductivity (kcf )

36.0

54.3

36.0

54.3

36.0

54.3

7.92 2.19 162.00 337.00

5.16

3.60

Kinematic viscosity (νcf × 103 )  2  m /h

Table 6.2. Cooling intensity of different media.

1.515

1.205

1.515

1.205

1.515

1.205

800.00 1594.90 875.60 900.10

990.80

998.20

kg/m3

Specific weight (γcf )

1465

1360

1046

970

515

479

589 531 211 155

1646

2715

Kh

54.0

50.1

38.6

36.7

19.0

17.6

21.7 19.6 7.8 5.7

60.6

100.0

In % of Kh for water

Cooling intensity

342 Tribology of Metal Cutting

Improvements of Tribological Conditions

343

the results of calculations of the cooling intensity Kh for some common cases in metal cutting. The summary of the results on the cooling action of the cutting fluid allows pointing out the following: • The cooling action of the cutting fluid assists the cutting process as far as it brings the cutting temperature closer to the optimal cutting temperature. Otherwise, the use of cutting fluid reduces tool life [42]. When one considers the whole machining system, the cooling action often stabilizes the temperature of the machining system components that results in better machining accuracy due to reduced thermal deformations of these components. Another down-to-earth but important aspect is the temperature of the part after machining. Often, when no coolant is used, this temperature is high so the operator finds it difficult to handle the part (including unloading, measurements and/or gaging). • Significant intensification of the cooling action of the cutting fluid is achieved by increasing its velocity, which has a dual result. First, it increases the convection heat transfer coefficient and second, high-velocity jets of the cutting fluid blow a boundary layer formed on high-temperature surfaces. This explains the efficiency of the high-pressure cutting fluid supply which increases the velocity of the cutting fluid. Although it is often claimed that the high-pressure supply of the cutting fluid increases its penetration ability into the tool–chip and tool–workpiece interfaces [43,44], in reality it is not so because, as it is shown in Chapter 3, the contact stresses are a way higher than the maximum pressure of the cutting fluid. It was conclusively proven that tool life (tool wear) does not significantly increase in cutting under very high static pressure [45]. In reality, high pressure of the cutting fluid increases its velocity, which, in turn, significantly improves the cooling action of this fluid. Moreover, it does not affect the cutting forces [46].

Cooling action due to evaporation. To comprehend the cooling action of the cutting fluid when it boils due to the contact with hot surfaces of the tool, one should consider the process of heat exchange between a solid and a boiling liquid [47]. The boiling process includes formation, growth and separation of bubbles. When the surface temperature is slightly hotter than the saturation temperature of the liquid, the excess vapor pressure is unlikely to produce bubbles. The locally warmed liquid expands and convection currents carry it to the liquid–vapor interface where evaporation takes place and thermal equilibrium is restored. Thus, in this mode, evaporation takes place at small temperature differences and with no bubble formation. As the surface becomes hotter, nucleate boiling takes place. As such, the excess of vapor pressure over local liquid pressure increases and eventually bubbles are formed. These occur at nucleating points on the hot surface where miniature gas pockets, existing in surface defects, form the nucleus for the formation of a bubble. As soon as a bubble is formed, it expands rapidly as the warmed liquid evaporates into it. The temperature of vapor in the bubbles is equal to the saturation temperature (θst ).

344

Tribology of Metal Cutting Table 6.3. Saturation temperature (θst ), heat of vaporization (rvo ), density of vapor (ρvo ), equivalent length (diameter or other length-scale) (beq ) for water vapor as functions of pressure (pat ).     θst (◦ C) ρvo kg/m3 beq × 106 (m) pat (MPa) rvo × 10−3 J/kg 0.01 0.02 0.04 0.06 0.08 0.10 0.20

45.8 60.1 75.9 85.9 93.5 99.6 120.2

2392 2357 2318 2293 2273 2257 2202

0.07 0.13 0.25 0.36 0.48 0.59 1.13

3836 954.6 289.6 137.4 79.4 50.6 14.2

This temperature depends on the properties of the liquid and pressure (Table 6.3), which remains invariable during the boiling process. For water vapor under the standard atmospheric pressure, this temperature is θst = 100◦ C. The buoyancy detaches the bubble from the surface and another starts to form. Nucleate boiling is characterized by vigorous bubble formation and turbulence. Exceptionally high heat transfer rates and heat transfer coefficients with moderate temperature differences occur in nucleate boiling, and in practical applications. Boiling is nearly always in this mode. The temperature of the boiling liquid in contact with the hot surface is equal to the temperature of this surface, θhs and then reduces with distance from this surface within the limits of the so-called boundary layer to a temperature slightly higher than θst . The pressure of the vapor within a bubble is higher than that of the surrounding. Due to this fact, this bubble grows to a certain size and then detaches from the surface. The diameter of the bubble, dbo at the instant of detaching is  dbo = 0.2ψb σo /(ρlo − ρvo ),

(6.11)

where σo is the surface tension, ρlo and ρvo are the densities of the liquid and vapor, respectively, ψb is the contact angle (Fig. 6.4), for kerosene ψb = 26◦ , for water ψb = 50◦ and for mercury ψb = 137◦ .

yb

Fig. 6.4. Contact angle.

Improvements of Tribological Conditions

345

The contact angle (ψb ) is a quantitative measure of the wetting of a solid by a liquid. It is defined geometrically as the angle formed by a liquid at the three phase boundary where a liquid, gas and a solid intersect, as shown in Fig. 6.4. Low values of ψb indicate that the liquid spreads, or wets well, while high values indicate poor wetting. If the contact angle is less than 90◦ the liquid is said to wet the solid. If it is greater than 90◦ it is said to be non-wetting. A 0◦ contact angle represents complete wetting. Two different approaches are commonly used to measure the contact angles of non-porous solids, i.e. goniometry and tensiometry. Goniometry involves the observation of a sessile drop of test liquid on a solid substrate. Tensiometry involves measuring the forces of interaction as a solid is in contact with a test liquid. When the wetting is good, the bubbles formed detach easily, whereas when the wetting is poor, the bubbles formed spread over the surface forming a vapor film. The greater the wetting, greater the ease with which the bubbles formed leave the surface frequently, higher is the heat transfer coefficient of this process, hbv . The frequency of separation from the surface and the number of bubbles formed as well as hbv depend on the temperature difference ∆θvp = θhs − θst . Figure 6.5 shows the dependence of the heat transfer coefficient on the boiling of water on the temperature difference ∆θvp under the atmospheric pressure of 0.1 MPa. When ∆θvp is small, the heat transfer process is the same as that due to convection (Zone 1 in Fig. 6.5). Then the heat transfer coefficient increases dramatically further increase in ∆θvp (Zone 2 in Fig. 6.5) because the frequency of bubble formation and the number of bubbles formed increase. The boiling regime corresponding to this state is called convective boiling. As the heating surface temperature rises, the rate of production of vapor bubbles becomes so high that eventually the surface becomes enveloped in a blanket or film of vapor which prevents the liquid from wetting the surface. When this happens, the insulating effect

hbv (W/(m2 °C)

104

103 1

2

3

4

102 0.1

1.0

10

100

∆qv p(°C)

Fig. 6.5. Dependence of the heat transfer coefficient of this process (hbv ) on the boiling of water on the temperature difference ∆θvp = θhs − θst .

346

Tribology of Metal Cutting

of the film greatly reduces the rate of heat transfer. As seen in Fig. 6.5 (Zone 3), after 4 2◦ reaching a certain maximum (for water) hmax bv = 4.65 × 10 W/m C under the critical cr ◦ temperature range ∆θvp = 20−25 C, the heat transfer coefficient reduces when ∆θvp increases further. Convective boiling becomes film boiling. Zone 4 (Fig. 6.5) corresponds to the stable film boiling. Here, the heat transfer coefficient shows practically no dependence on ∆θvp . The foregoing analysis suggests that the highest cooling effect is reached in Zone 3 so the design of the cooling system should be optimized to assure the operation in this zone. cr The maximum heat transfer occurs when hbv = hmax bv and ∆θvp = ∆θvp , so the maximum max cr specific heat flux can be written as qb−max = hmax bv ∆θvp . Because hbv and ∆θvp depend on the physical properties of the cutting fluid so that they differ for different cutting 4 2◦ fluids. For a wide range of water-based cutting fluids, (hmax bv = 4.65 × 10 W/m C cr ◦ and ∆θvp = 20 − 25 C), the maximum specific heat flux can be written as qb−max = 1.16 × 106 W/m2 .

As in the previous section, heat transfer parameters can be calculated using Eq. (6.7). The similarity numbers, however, should be considered as follows: • The thermal characteristic of the fluid in the Nusselt Number (Eq. (6.4)) should be taken at temperature θst . • Parameters beq and νcf in the Reynolds number (Eq. (6.3)) should be interpreted as follows: the equivalent length (diameter or other length-scale) beq is selected proportional to the diameter of the bubble, db formed on boiling; νcf = νvp is the conditional velocity of vapor, where νvp = qν−f /(rvo ρvo ), where qν−f isthe specific   heat flux into the liquid phase W/m2 , rvo is the heat of vaporization J/kg , and ρvo is the density of vapor at θst . Using the parameters introduced in Eq. (6.7), one can obtain p

hbv = cbv

kcfvo beq



∆θ rvo ρvo νvp

mvo

Pr nvo

(6.12)

Coefficient cbv , and powers pvo , mvo and nvo in Eq. (6.12) are shown in Table 6.4. To calculate heat transfer in the most practical case, where a water-based cutting fluid is supplied into the machining zone at the atmospheric pressure, Eq. (6.12) can be significantly simplified using the data presented in Tables 6.3 and 6.5 keeping in mind

Table 6.4. Coefficient cbv , and powers pvo , mvo and nvo in Eq. (6.12). Re ≤ 0.01 > 0.01

cbv

pvo

mvo

nvo

0.00390 0.00263

2.00 2.86

1.00 1.86

0.66 0.95

Improvements of Tribological Conditions

347

Table 6.5. Thermal conductivity (kcf ), thermal diffusivity (αcf ), kinematic viscosity (νcf ), volumetric expansion coefficient (βcf ) and Prandtl number (Pr) for dry vapor and water as functions of temperature.     αcf × 106 m2 /s θ (◦ C) kcf × 102 νcf × 106 m2 /s βcf × 104 (1/◦ C) Pr (W/(m◦ C)) Air 20 2.59 21.4 50 2.83 25.7 100 3.21 33.6 150 3.56 42.1 200 3.93 51.4 250 4.27 61.0 300 4.60 71.6 350 4.91 81.9 Water (along saturation line) 20 59.8 14.3 30 61.8 12.9 40 63.5 15.3 50 64.8 15.7 60 65.9 16.0 70 66.8 16.3 60 67.4 16.6 90 68.0 16.8 100 68.3 16.9

15.06 17.95 23.13 28.94 34.85 40.61 48.33 55.46 1.006 0.805 0.659 0.556 0.478 0.415 0.365 0.326 0.295

24.1 30.9 26.8 23.6 21.1 19.1 17.4 16.0 1.81 3.21 3.87 4.49 5.11 5.70 6.32 6.95 7.52

0.703 0.698 0.688 0.683 0.680 0.677 0.674 0.676 7.02 5.43 4.31 3.54 2.98 2.55 2.21 1.95 1.75

that in this case Re > 0.01 hbv = 170 (θhs − 100)1.86

(6.13)

Equations (6.12) and (6.13) are valid only for the temperature difference (∆θvp = θhs − θst ) corresponding to convective boiling. For water and water-based cutting fluids, this condition is valid when 105◦ C ≤ θhs ≤ 120◦ C. For other conditions, the heat transfer coefficient is calculated as If 120◦ C ≤ θhs ≤ 235◦ C, If θhs > 235◦ C,

then hbv

then hbv = 3.36 × 106 (θhs − 100)−1.43   = 3 × 103 W/m2 ◦ C

(6.14) (6.15)

Equations (6.13)–(6.15) are valid only when water is boiling under the atmospheric pressure and under natural convection. As discussed in the previous section, forced convection often takes place in real cutting systems. As such, the cutting fluid is forced to move over hot surfaces of tool, chip and workpiece. Such a movement brings changes in the boiling process. First, the natural

348

Tribology of Metal Cutting

value of the contact angle (Fig. 6.4) is changed. Second, the moving fluid detaches the partially formed bubbles from the surface being cooled before they reach the diameter defined by Eq. (6.11). Therefore, the flow of the cutting fluid makes the boiling process weaker so that heat transfer due to evaporation reduces. When the velocity of the cutting fluid is high, the heat transfer due to evaporation becomes negligibly small and thus “normal” heat transfer due to forces of convection takes place as discussed in the previous section. The opposite is true, however, when film boiling takes place. Here, the flow of the cutting fluid increases heat transfer because this flow blows a blanket or film of vapor which prevents the liquid from wetting the surface. Under the condition of film boiling, Zones 2–4 in Fig. 6.5 shift to the right, i.e. towards higher temperature differences. The higher the cutting fluid velocity, the greater the shift. To the first approximation, the heat transfer coefficient hcb in this case, can be calculated accounting for the combined contribution of the forced convection and boiling as If hbv < 0.5hcf ,

then hcb = hcf

If 0.5 ≤ hbv ≤ 2hcf , If hbv > 2hcf ,

then hcb =

then hcb = hbv

(6.16) 4hcf + hbv hcf 5hcf − hbv

(6.17) (6.18)

Cooling action of air–cutting fluid mixture (mist). As discussed at the beginning of this chapter, the cost of cutting fluid is approximately 16–17% of the life-cycle operational cost of machining. This cost continues to rise. It includes the costs associated with procurement, filtration, separation, disposal and record keeping. Already the costs of disposal of a cutting fluid are higher than the initial cost of this fluid, and they are still rising. Even stricter regulations are under consideration for cutting fluid usage, disposal and worker protection. As a result of all of this, the cutting fluid in wet machining operations is a crucial economic issue. An alternative, machining with “minimum quantity lubricant,” or MQL, is gaining acceptance as a cost-saving and environmental-friendly option in place of some wet machining processes. For example, spray cooling provides the benefits of the cutting fluid used in flood applications with the added performance of a high-velocity air–cutting fluid mixture. Therefore, it is of interest to consider heat transfer in the interactions of hot tool and workpiece surface and air–cutting fluid mixture. In cooling using an air–cutting fluid mixture, it becomes a case of two-phase cooling medium. Figure 6.6 shows spherical droplets having diameter ddr that moves with velocity νair towards a hot surface [47]. It is assumed that the concentration of droplets in the unit volume of the mixture is uniform. The temperature of the hot surface is θhs and that of the mixture is θmx . When a droplet meets the surface, it deforms so that the diameter of contact is Dct = mct ddr . As such, mct  1. The thermal energy entering a droplet first heats it to the saturation temperature, θst and then causes its evaporation. For the first part, heating, of this two-stage process the

Improvements of Tribological Conditions

349

vair

ddr

Ahs

Dct

Fig. 6.6. Graphical representation of droplets moving towards a hot surface.

balance equation is πd 3 πDct (θst − θmx ) τ1h hcf = Cp−cf ρcf dr (θst − θmx ) , 4 6

(6.19)

where τ1h is the time of heating. Thus this time can be expressed as τ1h =

2 Cp−cf ρcf ddr 3 hcf mcf

(6.20)

For the boiling and evaporation 3 πddr πDct (θhs − θst ) τ2h hvb = ρcf rvo , 4 6

(6.21)

where τ2h is the time of boiling and evaporation, which can be expressed as τ2h =

ρcf rvo ddr 2 3 hvb m2ct (θhs − θst )

(6.22)

As the mean heat transfer coefficient for the whole process can be represented as h1−2 =

hcf τ1h + hvb τ2h τ1h + τ2h

(6.23)

350

Tribology of Metal Cutting

then substituting Eqs. (6.20) and (6.22) into Eq. (6.23), one can obtain h1−2 =

  hcf hvb Cp−cf (θhs − θst ) + rvo rvo hcf + Cp−cf hvb (θhs − θst )

(6.24)

The number of droplets falling simultaneously on the hot surface having an area Ahs depends on the concentration Kdr of liquid in the two-phase mixture. As it was assumed, the concentration of droplets in the unit volume (m3 ) of the mixture is uniform, this number is calculated as ndr−V =

6Kdr 3 πddr

(6.25)

and on the surface of unit area (m2 ) it is ndr−A =

√ 3

ndr−V

2

1 = 2 ddr



6Kdr π

2/ 3 (6.26)

2 , the total area As the area of the total surface Ahs taken by one droplet is 0.25πm2ct ddr taken by all the droplets at any time instant is 2 Ahs−dr = 0.25πm2ct ddr ndr−A Ahs

(6.27)

The heat transfer process with the heat transfer coefficient h1−2 takes place over the area Ahs−dr of the total surface area Ahs . On the rest of this surface (over the area Ahs − Ahs−dr ), the heat transfer takes place with the air contained in the two-phase mixture. The heat transfer coefficient in this process is designated as hair . The total combined heat transfer coefficient for the two-phase mixture is calculated as hc−mix =

  h1−2 Ahs−dr − hair Ahs − Ahs−dr Ahs

(6.28)

or   2 3 hc−mix = 1.2Kdr/ m2ct h1−2 − hair + hair

(6.29)

Heat transfer coefficients in this equation are calculated using the above-described methodologies. When boiling takes place in rather thin surface films of the cutting fluid, whose thickness is close to the diameters of bubbles formed on boiling (dbo , Eq. (6.11)), then the heat transfer coefficient hbv would depend on the thickness of the surface film, δsf .

Improvements of Tribological Conditions

351

Reznikov and Resnikov [47], for the surface films having a thickness δsf ≤ 5 × 10−3 m, proposed the following correction factor   χcor = 1.25 exp −40δsf

(6.30)

which is to be used as a multiplier in Eqs. (6.13)–(6.15). Because in the practice of machining the thickness δsf = (0.5–10) × 10−3 m, then for many practical cases χcor = 1.20–1.23. Cooling action due to heat pipe embedded in the tool. Heat pipes are sometimes used to cool down the cutting tools [48,49]. Although the theory of heat pipes is well developed [50,51], there is no simple methodology to calculate the cooling action of heat pipes that can be used in the practice of tool design. The heat pipe (Fig. 6.7) basically consists of a thick-walled hermetic container (1) made up of a high thermal conductivity material. The container encloses some amount of the easy-to-evaporate working fluid. One end (often called as the evaporator) of the container is embedded in the unit to be cooled (2) while the other end (often called as the condenser) contains a heat exchanger (radiator) (3) to release the thermal energy to the surrounding. Heat applied by a heat source at the evaporator region vaporizes the working fluid in that section. This also creates a pressure difference that makes the vapor to flow from the

2

qout

hv2

qhs2

3

dh−in

Lhp

dh−ex 1

qhs1

hv1

qin qh1

Fig. 6.7. Model of a vertical heat pipe.

352

Tribology of Metal Cutting

evaporator to the condenser where it condenses releasing the latent heat of vaporization. The condensed working liquid then returns to the evaporator. This process is capable of transporting the heat from a hot region to a cold region. The heat pipe transports large amount of heat with a small temperature difference. The balance equation for internal surface of the container is constructed assuming that this container is thermo insulated so that there is no heat exchange with the surrounding regions between the “hot” and “cold” zones. Thus, hbl Abl (θhs1 − θst ) = hcd Acd (θst − θhs2 ) ,

(6.31)

where hbl and hcd are the heat transfer coefficients in the boiling and condensation zones, respectively, θhs1 and θhs2 are the average temperatures in the boiling and condensation zones, respectively, Abl and Acd are the areas of boiling and condensation zones, respectively. The left side of this equation is the amount of thermal energy that enters from the walls of the container into the boiling liquid in the “hot” zone while the right side is that released through the walls in the “cold” zone. For the vertical container shown in Fig. 6.7 2 Abl = πdh−in hν1 + 0.25πdh−in

(6.32)

2 Acd = πdh−in hν2 + 0.25πdh−in

(6.33)

To determine the heat transfer coefficient in the boiling zone, one can use Eq. (6.12) representing it in the following form hbl = Θ1 (θhs1 − θst )mvo

(6.34)

where p

Θ1 = cbv

kwfvo



Pr nvo

beq−wf rwf ρwf νwf

mvo

(6.35)

Values of the physical characteristic of working liquid and its vapor in Eq. (6.35) are taken at temperature θst . The heat transfer coefficient on condensation can be determined using a simplified model. The condensed liquid usually appears as liquid droplets (poor wetting) or film. In the cooling of cutting tools, good wetting surfaces for heat tube are usually used so as to consider the surface condensation. All the thermal energy formed on condensation of vapor is transferred into the surface (of temperature θhs which is lower than the temperature of vapor, θst ) through the film of condensed liquid. Because the flow in this film is normally laminar, it can be accepted that heat transfer takes place due to thermal conductivity. Consider an infinitively small element ∆x of the surface film condensed on a vertical surface of a body (Fig. 6.8). As thickness of the film, δx is small, the temperature

Improvements of Tribological Conditions

353

dx

x

Lfl ∆x qst qhs

X Fig. 6.8. Model of film condensation.

gradient across this film can be thought of as (θst − θhs ) δx and thus, according to the Fourier law of heat conduction, the specific heat flux through this film is qx = kwf

(θst − θhs ) , δx

(6.36)

where kwf is the thermal conductivity of the working fluid corresponding to the average temperature 0.5 (θst − θhs ). Because the specific heat flux is qx = hx (θst − θhs ), the heat transfer coefficient is calculated as hx = kwf /δx

(6.37)

As it follows from Eq. (6.37), the determination of the heat transfer coefficient reduces to that of the thickness of the film condensed on the surface, δx . Nusselt, compiling a great body of experimental data, proposed the following equation [47]  δx =

4kwf µwf (θst − θhs ) 2 r g ρwf wf

1/ 4 x

,

where µwf is dynamic viscosity of the working fluid, µwf = νwf ρwf .

(6.38)

354

Tribology of Metal Cutting

Substituting Eq. (6.38) into Eq. (6.37), one can obtain  hx = 1.25

2 r k3 ρwf wf wf

1/ 4 (6.39)

µwf (θst − θhs ) x

For practical calculations, it is necessary to determine the average heat transfer coefficient, hcd over the total length Lfl , of the hot surfaces in contact with the condensed film of the cutting fluid as

hcd

1 = Lfl



Lfl hx dx = 1.67 0

1/ 4

2 r k3 ρwf wf wf

µwf Lfl (θst − θhs )

(6.40)

As before, ρwf , kwf , and µwf in Eq. (6.40) should be considered at the temperature 0.5(θst − θhs ). Equation (6.40) is obtained for a vertical wall. If vapor is condensed on a surface inclined at an angle ϕcd to a horizontal plane, then the heat transfer coefficient is calculated as  hcd = 1.67

2 r k 3 sin ϕ ρwf wf wf cd

1/ 4 (6.41)

µwf Lfl (θst − θhs )

and for a horizontal tube having diameter dfl it is calculated as  hcd = 1.28

1/ 4

2 r k3 ρwf wf wf

(6.42)

µwf dfl (θst − θhs )

By analogy with Eqs. (6.34) and (6.35), the heat transfer coefficient for condensation can be represented as hbl = Θ2 (θst − θhs2 )−0.25

(6.43)

where  Θ2 = 1.67

2 r k 3 sin ϕ ρwf wf wf hp

µwf hν2

1/ 4 ,

(6.44)

where ϕhp is the inclination angle of the heat pipe, ρwf , kwf and µwf are considered at the temperature 0.5(θst − θhs2 ).

Improvements of Tribological Conditions

355

Substituting Eqs. (6.34) and (6.43) into Eq. (6.31), one can obtain  θhs1 =

Θ2 Acd Θ1 Abl



1 mvo +1

0.75

(θst − θhs2 ) mvo +1 + θst ,

(6.45)

2 where the ratio Θ Θ1 depends on the properties of the evaporated fluid, saturation temperature and the temperature on the inner wall of the hot tube in the condensation zone. Because for a given type of the working fluid, the saturation temperature θst is completely 2 determined by the pressure in the container, pin−c (MPa) then Θ Θ1 = f(pin−c θhs2 ), i.e. the efficiency of the hot pipe is determined by the level of vacuum inside the container, type of the working fluid and by cooling intensity of its condensation zone. Approximation of the available experimental data allowed [47] to obtain the following relation

θhs2 − θst ≤ 14.2p−0.15 in−c

(6.46)

It is understood that Eq. (6.45) is an approximation because the real thermal process in the heat pipe is more complicated compared to that considered in the derivation of this equation. However, it can be used in many engineering calculations involved in the cutting tool design. An example of a tool design with the heat tube is shown in Fig. 6.9. The cutting insert (1) is cooled by the heat pipe (2) imbedded in the holder (3). The heat from the cutting insert is transferred to the “hot” end of the heat pipe and then transferred by the vapor of the working fluid to the “cold” end of the heat pipe, where it is dissipated by the radiator (4). As seen, the tool design is very simple. The use of such tools can be very efficient in dry cutting. Moreover, the efficiency of such tool can be significantly improved if radiator (4) is a part of the machine tool circulation cooling system. Embrittlement action. The embrittlement action of the cutting fluid reduces the strain at fracture of the work material. This action is based on the Rebinder effect [52]. This effect was invoked as early as in 1936 as the basis of “oiliness” of boundary lubricants. Conducting tension studies of tin specimens, Rebinder observed that a boundary-lubricant film of oleic acid lowered the stress and stress at fracture. Microscopic examination of

1

3

2

Fig. 6.9. Tool with a built-in heat tube.

4

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Tribology of Metal Cutting

the test specimens showed a great increase in the number of active slip planes. He concluded that this resulted from the penetration (absorption) of the surface active acid into microcracks which lowered the strength of the specimen. Rebinder’s studies were directly concerned with the metal cutting process. Conducting a great number of cutting tests under different cutting conditions and with different cutting fluids, he observed microcracks formation and “healing.” The latter was particularly pronounced in machining ductile materials, where great plastic deformation of the layer being removed is observed. The results of Rebinder’s study showed that the absorbed films prevent the closing of microcracks (healing due to plastic deformation of the work material). Because each microcrack in the machining zone serves as a stress concentrator, smaller energy was required for cutting. Pursuing this direction, Epifanov [53] found that the penetration of the foreign atoms (from cutting fluid decomposition) produced an embrittlement effect in a manner similar to hydrogen embrittlement. He concluded that it thus facilitated by a resulting decrease in plasticity. Our current understanding of the Rebinder effect is that the alternation of the mechanical and physical properties of materials is due to the influence of various physiochemical processes on the surface energy [52]. The energies of the process which lead to the formation of a new fracture surface was considered by Griffith [54], who developed the equation which defines the thermodynamic requirements for fracture " σf =

2γsf E , πccr

(6.47)

where σf is the fracture stress, γsf is the surface energy, E is the Young’s modulus and ccr is the length of some pre-existing crack. Griffiths’ equation assumes that the only process that absorbs energy during fracture is the energy required to form a new surface. As follows from this equation, the surface energy reduces from a certain level γsf −1 to a new level γsf −2 due to the penetration of the foreign atoms (from cutting fluid decomposition) then the energy required for fracture  1/2 reduces by γsf −1 /γsf −2 . At this point one may wonder if pre-existing cracks exist at the surface of ductile work materials. Multiple observations on the surface conditions show that there are many cracks existing on the surface of even very ductile materials. For example, Fig. 6.10 shows a micrograph of partially formed chip (ductile work material – AISI steel 4330), where a number of very deep cracks exists on the surface of the layer being removed. The Rebinder effect takes place for practically all solids and structures. Its occurrence depends on many physiochemical factors like the chemical composition of solid and fluid, deformation and fracture conditions (strain, velocity, state of stress, material structure), etc. Depending upon a particular combination of the conditions, the Rebinder effect manifests itself in different ways: from lowering the shear flow stress to a significant reduction of strength (both the stress and strain at fracture). The thermodynamic condition for the Rebinder effect to lower the strength of a material is that the intensity of surface interactions should be comparable with the energy of atomic, ion and/or

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Fig. 6.10. Quick-stop micrograph of partially formed chip showing great number of surface cracks. Work material – AISI steel 4340. Etched with 10 ml Nital and 90 ml alcohol.

molecular bonding in this material. Experience [45] shows that for a majority of the materials used in the industry, a noticeable reduction of the strength occurs when the energy of surface interaction reaches 50–100 kJ/mol. Lowering the surface energy of a solid leads to alternation of its mechanical properties which can be achieved as a result of adsorption, chemisorption, surface electrical polarization, surface chemical reactions, etc. Understanding the physiochemical processes listed is of vital importance for the metal cutting tribology, development and application of cutting fluids because the course of these processes in each particular case of machining defines to a large extent the resistance of the work material to cutting. On the other hand, however, these processes correlate with tribological processes at the tool–chip and tool–workpiece interfaces as far as they reduce the energy spent in cutting. Because a detailed explanation of the nature of the Rebinder effect is a subject of a book on applied physics, only a short description of some of the processes involved in this effect is provided, accounting for the objective of this book. Physical adsorption (physisorption) is adsorption in which the forces involved are intermolecular forces (van der Waals-type forces) of the same kind as those responsible for

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the imperfection of real gases and the condensation of vapors, and which do not involve significant change in the electronic orbital patterns of the species involved. Physical adsorption reduces strain and stress at fracture as well as strain hardening of solids. Calculations [45] show that maximum reduction of the surface energy of a solid due to physical absorption does not exceed 10% for common metals. This is because large organic molecules of surface-active agents (SAA) cannot penetrate deep enough into microscopic surface cracks and thus their action is limited by a molecular layer of SAA. However, the adsorption of organic SAA can lower the fracture strength of solids having low bonding energy, i.e. low melting temperature metals, some ionic crystals and polymers. Physical adsorption of SAA is widely used in deforming processes where no fracture takes place so the molecular layer of SAA leads to greater plasticity of the surface layer that is extremely important due to high contact friction. In metal cutting, where fracture should take place, the conditions of deformation and fracture are much more severe so physical adsorption cannot be considered as a decisive factor in lowering the work material resistance. Chemical adsorption (chemisorption) is adsorption in which the forces involved are valence forces of the same kind as those operating in the formation of chemical compounds. Chemisorption can be considered as a chemical bond, involving substantial rearrangement of electron density, which is formed between the absorbate and the substrate. The nature of this bond may lie anywhere between the extremes of vitally complete ionic or complete covalent character [55,56]. This process is much more desirable in metal cutting. As discussed in Chapter 1, fracture occurs in each chip formation cycle so new juvenile surfaces are formed. Atoms on such surfaces are chemically active and can chemically react with molecules of organic SAAs contained in the cutting fluid. Because the energy of surface interaction due to chemisorption reaches dozens or even hundreds of kJ/mol, the free surface energy reduces substantially. Chemisorption processes often include mechanochemical processes resulting in the formation of reactive radicals. This takes place due to the electrons emitted from fresh surfaces and/or due to cathodic decomposition of organic molecules at the newly formed juvenile surfaces. When chlorine- and iodine-substituted organic SAAs are used as additives in cutting fluids, the nature of formation of active agents is different. The influence of halogensubstituted compounds on the cutting process is shown in Fig. 6.11. The efficiency of the cutting fluid compared to dry cutting was judged by an increase in the cutting feed under a given feed force, i.e. Kf = ((fcf − fdr )/(fcf ))100%, where fcf is the feed achieved with the cutting fluid and fdr is the feet under dry cutting. As seen in Fig. 6.11, the maximum efficiency of the cutting fluid is achieved only when the feed force Fax exceeds a certain critical value. The critical value of Fax depends on the chemical structure of a molecule of SAA added to the cutting fluid. Figure 6.12 shows that, under constant cutting speed, the values of Fax correlates linearly with the energy Uf required for breaking carbon–halogen bonds (by the radical mechanism). Calculations [45] show that when the critical Fax is achieved, the stresses in the deformation zone become great enough to destruct SAA molecules. In other words, the

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Kf (%)

80

60

40

20

160

200

180

220

Fax (N )

Fig. 6.11. Influence of feed force (Fax ) on relative cutting feed (Kf ). Longitudinal turning, work material – AISI steel 1045, cutting speed ν = 2.9 × 10−3 m/s, depth of cut dw = 0.8 mm, cutting fluid – alpha-tosyl-l-lysine chloromethyl ketone (TLCK).

Uf (kCal/Mole) 90

70

50

30 195

295

Fax (N )

Fig. 6.12. Influence of axial force (Fax ) on destruction energy (Uf ) of the cutting fluid molecules. Longitudinal turning, work material – AISI steel 1045, cutting speed ν = 2.9 × 10−3 m/s, depth of cut dw = 0.8 mm, active agents – tetrachloride, chloroform, iodine, methylene iodine, chloroform, methylene chloride, benzyl chloride and benzyl iodide.

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critical stress activates mechanochemical processes that result in the formation of reactive radicals, which lower the energy of deformation and fracture of the work material. The occurrence of the mechanochemical process discussed and chemisorption interactions explains the efficiency of some organic fluids (as oleic acid, carbon tetrachloride) as well as organic acids, sulfur, iodine, phosphorous and chorine compounds as widely used additives to cutting fluids. Formation of surface compounds is very close to chemisorption by the character and intensity of energy interactions. As a result of relatively low-energy chemical reactions they undergo exchange, oxidation–reduction and form of coordinated compounds. Normally it is sufficient that the free energy of reaction reaches 50–100 kJ/mol. Any further intensification of such a reaction does not lead to improvements in machining because the active particles (atoms, ions and molecules) firmly bond to the surface loosing mobility and in-depth penetration ability. For example, when drilling nickel having a free surface energy of only 63 kJ/mol, the strongest influence is shown by mercury chloride and iodine–ethanol solution (Table 6.6). When machining quartz, the strongest influence is shown by base solutions and aqueous solutions of hydrofluoric acid. When machining aluminum oxide ceramics, non-organic salts showed the best result. To achieve the strongest effect, high concentrations of active additives are needed. When drilling nickel, the maximum effect was observed when a 20% concentration of iodine in ethanol was used. However, to achieve the cutting feed lower only by 20%, compare the maximum achieved at that concentration, an order lower concentration of iodine is sufficient as it follows from Fig. 6.13. Copper–ammonium complexes can significantly reduce the surface energy. For example, its application resulted in a 3-fold increase in the allowable cutting feed in the drilling of alloyed α-brass due to the following low-energy chemical reaction: Cu + [Cu(NH3 )4 ]2+ = 2[Cu((NH3 )2 ]+ . The maximum effect of copper–ammonium complexes depends on their concentration and on particular cutting conditions. Figure 6.14 shows that the effect of application of a copper–ammonium complex in drilling begins to appear only under certain concentrations and, moreover, this effect depends on the force applied to the drill.

Table 6.6. Influence of various media on the cutting feed in drilling of nickel. Medium

Active additive concentration (mol/l)

Water Ethanol Solution of I2 in ethanol Aquatic solutions: Hg(NO2 )2 HgCl2 HCl

Cutting feed (mm/s)

Improvement

fcf −fdr fdr

× 100%

No cutting fluid (fdr )

With cutting   fluid fcf

– – 1

0.18 0.18 0.16

0.21 0.20 0.53

16 11 230

0.5 0.2 1

0.18 0.20 0.12

0.17 0.75 0.12

−5 275 8

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Kf (%)

200

150

100

50

0 −5

−4

−3

−2

−1

0

1 logCcf

Fig. 6.13. Influence of active agent concentration (Ccf ) on relative cutting feed (Kf ) for iodine solution in ethanol. Drilling high nickel alloy, the applied axial force Fax = 150 N.

Kf (%) 3 300

200

2

100 1 0

5

10

15

Ccf (%)

Fig. 6.14. Influence of concentration (Ccf ) of copper–ammonium complex on relative cutting feed (Kf ) in drilling α -brass. The applied axial force: (1) 120 N, (2) 180 N and (3) 240 N.

Copper–ammonium complexes have even more pronounced effect in machining difficultto-machine high nickel alloys, for example in machining Nitinol (composed of a nearly equal mixture of nickel (55 wt%) and titanium). In this case, the use of copper–ammonium complex [Cu(NH3 )4 (H2 O)2 ]2+ resulted in many fold increase in the allowed cutting feed and in significant reduction in the specific work of drilling when the optimum cutting conditions are used (Table 6.7). High effectiveness of this complex is due to low-energy

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Table 6.7. Influence of various media on the drilling parameters. Work material – Nitinol. Drilling parameter

Medium Air

Water soluble oil Oleic acid Tetraammonium

Cutting feed (f × 104 (sm/s)) 1.7 Drilling torque (Mdr × 106 (N/sm)) 35 Specific work of drilling 98 (Wdr × 10−2 (J/sm3 )) Effectiveness compared to air 1.0

3 20 29

5.3 3.1 2.7

3.4

36

33 11.1 1.5 65

chemical reaction: Ni + 2[Cu(NH3 )4 (H2 O)2 ]2+ = Ni2+ + 2Cu + 8NH2 + 4H2 O. In the case considered as well as in the above-considered case of drilling brass, the effectiveness of copper–ammonium complexes depends on the machining regime under given tool geometry which defines the cutting force. As follows from the data presented in Fig. 6.15, the maximum effectiveness is achieved under a certain axial force (and thus the cutting force) in drilling. Some important conclusions can be drawn from the consideration of the Rebinder effect as applied to the actions of cutting fluids in metal cutting: • The efficiency of a particular cutting fluid depends to a large extent on the surface energy of the workpiece and on the configurations of pre-existent cracks on Kf (%) 3

200 2

100

4

2.65

1

2.90

3.75

logn

Fig. 6.15. Influence of drill rotational speed (n(rpm)) on relative cutting feed (Kf ) in drilling Nitinol in the copper–ammonium complex solution. The applied axial force: (1) 270 N, (2) 440 N, (3) 600 N and (4) 800 N.

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the surface. It explains a great scatter in cutting fluid application data even for the same machining operation and for the same work material. To achieve more consistent results, the design of machining operation should include a consideration of the above-mentioned parameters. • The composition and chemistry of cutting fluid should be designed accounting for the Rebinder effect rather than on other properties of a particular cutting fluid. • Because the Rebinder effect involves chemical reactions, it requires some time for these reactions to complete. It explains the known fact that the efficiency of cutting fluids with organic SAA greatly reduces when the cutting speed exceeds 150 m/min. Unfortunately, a few known attempts to comprehend the Rebinder effect in metal cutting literature were not successful. For example, Shaw in his book [37] attempted to present the Rebinder effect. Unfortunately, the whole concept of this effect was misunderstood: • The section title is “Shear Plane Action.” In reality, the Rebinder effect has practically nothing to do with the shear plane action because it reduces the stress and strain at fracture. This is the major point missed. • It is stated that this effect may take place only at very low cutting speed. In reality, only some initial experiments, presented in the literature sources cited in this book, were carried out at low cutting speeds as it is normally done in metal cutting to gain initial knowledge on the mechanics and physics of the process. For example, Zorev’s book, edited by Shaw [25], contains Chapter 2 “Experimental Studies of Chip Formation and Contact Processes on the Tool Face at Low Cutting Speeds.” Unfortunately, further tests at high cutting speeds and their results were not considered by Shaw. • The section states that “A large number of microcracks is assumed to be produced in the chip at the cutting edge when surface is generated.”(page 311 in [37]). None of the sources dealing with the Rebinder effect and cited in Shaw’s book contains this misleading statement. Rather, the pre-existing microcracks on the free surface of the layer to be removed were dealt with. It is too late to rely on the microcracks in the chip because it would not affect its formation and thus deformations, forces, temperatures, etc. • The section states (page 311 in [37] that “This action has been termed ‘harness reduction’ in the USSR.” In reality it was “strength reduction.” This is not just an issue of the terminology or translation. Rather, the whole concept of the Rebinder effect can be understood properly if one realizes that this is a universal fundamental physical effect taking place whenever plastic deformation and fracture occur. Fortunately, there is always a lucky exception. The Rebinder effect and its importance in cutting were discussed in an excellent book on cutting fluids selection and application published by the SME metalworking fluids subdivision [57], where it was suggested that “it seems possible that most of the effects formerly ascribed to EP lubricant action on the part of chlorine, sulfur, and other boundary and EP types of fluids, will emerge as primary due to shear–stress reduction of the workpiece metal during machining.”

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Unfortunately, cutting fluid companies and researchers in the field missed this important suggestion continuing to promote EP additives as having direct impact on the tool– chip contact. As such, the relevant tribological conditions like contact pressures and temperature are not considered in terms of justification of physical possibility of this impact.

6.1.5 Types of cutting fluids There are five major types of cutting fluids available today: • straight cutting oils – waterless. • soluble oils – emulsions. • synthetic fluids. • semi-synthetics (semi-chemical) – micro emulsions. • cryogenic fluids Utilization of various types of cutting fluids in US is shown in Fig. 6.16. Straight oils are series of products which contain “no water” and are used in applications where a great deal of work materials is to be removed in short time as in milling, drilling, turning, broaching, gear hobbing and threading. A straight cutting oil consists of the base oil to which one or more mineral oils are added to achieve a specific viscosity. Two basic categories of base oils are used: naphthenic mineral oils and paraffinic mineral oils. In the formulation of straight cutting oils, mineral oils account for 80% of the total formula. The other components of straight cutting oils are as follows: chlorinated paraffin, active sulfur carriers, inactive sulfur carriers, friction modifiers, tackiness modifiers, viscosity index modifiers, anti-weld additives, odorants and polar additives.

Straight Oils - 23%

Synthetic - 12%

Soluble Oils - 46%

Semi-Synthetic - 19%

Fig. 6.16. Utilization of cutting fluids in US.

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Straight cutting oils generally contain what are called extreme pressure or anti-weld additives such as chlorine and sulfur. It is believed that these additives react under pressure and heat to give the oil better lubricating characteristics. Straight cutting oils are most often used undiluted. Occasionally they are diluted with mineral oil, kerosene or mineral seal oil to reduce either the viscosity or the cost. They will not mix with water and will not form an emulsion with water. The advantages of straight cutting oils are good lubricity, effective anti-seizure qualities, good rust and corrosion protection, and stability. Disadvantages are: poor cooling, mist and smoke formation at high cutting speeds, high initial and disposal costs. Straight cutting oils perform best in heavy duty machining operations and very critical grinding operations where lubricity is very important. These are generally slow speed operations where the cut is extremely heavy. Some examples are broaching, threading, gear hobbing, gear cutting, tapping, deep-hole drilling and gear grinding. Straight cutting oils do not work well in high-speed cutting operations because they do not dissipate heat effectively. Because they are not diluted with water and the carryout rate on parts is high, these oils are costly to use and, therefore, only used when other types of cutting fluids are not applicable. Unless contaminated with water, these types of cutting fluids contain no bacteria to promote rancidity. Water emulsifiable oils. More commonly referred to as soluble oils. This, however, is a misnomer because they are not really soluble in water but rather form an emulsion when added to water. These emulsifiable oils are oil-based concentrates, which contain emulsifiers that allow them to mix with water and form a milky white emulsion. Emulsifiable oils also contain additives similar to those found in straight cutting oils to improve their lubricating properties. They contain rust and corrosion inhibitors and a biocide to help control rancidity problems. Advantages of water emulsifiable oils are: good cooling, low viscosity and thus adequate wetting abilities, non-flammable and non-toxic, easy to clean from small chips and wear particles using standard filters, relatively low initial and disposal costs. Disadvantages are: low lubricity, rancidity, misting, low stability (components have different degradation levels), in mass production require everyday expensive maintenance in order to keep the required composition. Water emulsifiable oils are the most popular cutting fluids in use today. Because they combine the lubricating qualities of oil with the cooling properties of water they can be used in a wide range of machining and grinding operations. Synthetic fluids. Sometimes referred to as chemical fluids, these synthetic cutting fluids are water-based concentrates, which form a clear or translucent solution when added to water. These fluids contain synthetic water-soluble lubricants, which give them the necessary lubricating properties. In addition, these synthetic fluids contain rust and corrosion inhibitors, biocides, surfactants and defoamers. Synthetic cutting fluids do not contain any oil. Advantages of synthetic cutting fluids are: resistance to rancidity, low viscosity and thus good cooling and wetting, good rust protection, little misting problems, nontoxic, completely non-flammable and non-smoking, good filtration with standard filters and biodegradable. Disadvantages are: insufficient lubricity for heavy duty applications, reaction with non-metallic parts and residue is often a problem. As disposal problems have become an ever increasing problem with the advent of the Resource Conservation

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and Recovery Act, synthetic fluids, as they present less of a disposal problem than emulsifiable oils, have become more popular because synthetics are easier to treat than emulsifiable oils before they can be disposed. Synthetics are most definitely the products of the future. A very large percentage of the development work on cutting fluids is devoted to improving the synthetic fluid technology. However, there are still some problems and some machining and grinding operations that for one reason or the other cannot be done using a synthetic fluid. The major problem is that lubrication has always been the big problem for synthetic coolants. Another problem caused by synthetics is the sticky and gummy residue that is sometimes left when water evaporates from the solution mix. Metal safety on non-ferrous metals is a problem with some synthetics because of their relatively high pH (8.5–10.0) and the lack of oil to act as an inhibitor. Semi-synthetic fluids. These are synthetic fluids, which have up to 25% of oil added to the concentrate. When diluted with water, they form a very fine emulsion that looks very much like a solution, but in fact, is an emulsion. The oil is added to improve lubricity. When synthetic fluids were in their early stages, lubricity was a big problem, so semisynthetics were introduced. Many users feel more “comfortable” using a cutting fluid which contains at least some mineral oil because it applies a protective and lubricating film of oil on the machinery [11]. The choice of a semi-synthetic cutting fluid can offer an ideal compromise to the user who would like to diminish the use of soluble oil coolants, yet is uncomfortable or unable to take advantage of true solution synthetic cutting fluids. Semi-synthetic cutting fluids are essentially hybrids of soluble oil and synthetic coolant chemistries. The amount of intermixing of chemistries is dependent upon the final characteristics desired for the semi-synthetic. In seeking to achieve soluble oil traits, soluble oil chemistries would predominate with a minor input of synthetic fluid chemistry. The result would be a semi-synthetic cutting fluid that behaves similarly to soluble oil without the significant petroleum oil content. At the other end of the spectrum, semi-synthetics are required to behave like synthetic fluids predominantly utilizing solution-type chemistry. The result is a cutting fluid exhibiting primarily synthetic fluid tendencies with minimal presence of mineral oil. Like all cutting fluids, semi-synthetics are required to lubricate, cool and protect metal parts and machinery. A variety of generic chemistries are used to accomplish these objectives [11]. To provide lubrication, the semi-synthetic cutting fluid first and foremost employs petroleum oil, the common denominator for all semi-synthetics. Not only does mineral oil provides a diluent for the fluid chemicals, it also provides a certain degree of boundary lubrication. Typically, the lubrication properties are enhanced by other chemical lubricants common to soluble oil or synthetic fluids. For example, synthetic hydrocarbons, polyols and esters are generally used not only to augment the lubrication properties of semi-synthetic fluids, but also to provide a diluent for additives. In order to solubilize or emulsify the lubricants into the water, emulsifying chemicals are required. Most of the commonly used materials are borrowed from soluble oil chemistries. Typical emulsifiers employed are non-ionic surfactants such as polyethers, amine soaps, petroleum sulfonates and amine condensates. Many of these chemicals

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provide emulsification of the lubricant, and also the anti-corrosion properties necessary for any water-dilatable cutting fluid. The complete chemical package for a semi-synthetic fluid also includes miscellaneous additives which are mixed into the cutting fluid to provide specific properties. These can vary from phosphorous, sulfur or chlorine additives to wetting agents, defoamers and biocides as required. Clearly, the formulation of semi-synthetic cutting fluids is a smorgasbord of chemistries picked and chosen from both soluble oils and synthetic fluid technologies. The types and influences of the two technologies when combined form a hybrid cutting fluid exhibiting various degree of characteristics from these two classes of cutting fluids. Liquid nitrogen. Liquid nitrogen (having temperature –196◦ C) is used as a cutting fluid for cutting difficult-to-machine materials including high titanium and nickel-based alloys, where chip formation and chip breaking present a significant problem [58–61]. Liquid nitrogen is used to cool workpiece (for example, internally supplied under pressure in the case of tube-shaped workpieces), to cool the tool (which has the internal channels through which liquid nitrogen is supplied under pressure) or by flooding general cutting area. Although the required properties of the cutting fluid should be formulated for each particular machining operations, it is believed that some of the qualities required in a good cutting fluid could be listed as: (a) good lubricating qualities to reduce friction and heat generation, (b) good cooling action to effectively dissipate the heat generated during machining, (c) effective anti-adhesion qualities to prevent metal seizure between the chip and the rake face, (d) good wetting characteristics which allow the fluid to penetrate better into the contact areas as well as in the cracks, (e) should not cause rust and corrosion of the machine components, (f) relatively low viscosity fluids to allow metal chips and dirt to settle out, (g) resistance to rancidity and to the formation of a sticky or gummy residue on the parts or machines, (h) stable solution or emulsion, (provide safety work environment (non-misting, nontoxic, non-flammable (smoking)), (i) should be economical in use (including maintenance), filter and dispose. If there was one product that met all the particular requirements to the cutting fluid, the selection of a cutting fluid would be easy. But there is no such product. Moreover, many of the above-listed properties often cannot be guaranteed without actual testing of a particular cutting tool in a particular production environment. Such a testing, however, is expensive and time consuming. Therefore, a method to compare different cutting fluids for a particular machining operation should be beneficial. Although a number of attempts

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to develop such a method have been made (for example, [35,62–64]), no method has been developed for qualifying and comparing the performance of one cutting fluid to another [22,65].

6.1.6 Practical consideration in the final selection Once a group of possible cutting fluids has been selected, the coolant user (buyer) should bench test and evaluate the candidates according to the user’s test procedures and criteria. Each shop or company has its own methods of bench testing or particular parameters to be met. There are, however, several basic considerations in the final selection of cutting fluids [11]: Waste treatability. This factor is listed first because many plants and machine shops have already established such a procedure so as to, consider waste treatability as the chief criterion in selecting a cutting fluid [22]. Most manufacturing facilities must pretreat waste water prior to discharge. Because cutting fluids for metalworking may easily represent a significant percentage of a plant’s waste water, it has become critical that the waste treatment of the prospective cutting fluid can be handled using the established procedure(s) of treating waste. The Environmental Protection Authority (know as the EPA) has been putting increasing pressure on local and state environmental agencies to enforce the Clean Water Act. As a result, local Publicly Owned Treatment Works (POTWs) have been much more vigorous in monitoring industrial sites for their discharges. Because: (a) establishing the cutting fluid disposal system in the existing plant is a painstaking effort, (b) equipment bought to support this system is expensive, (c) pressure from POTWs is mounting, many manufacturing and plan managers are placing main emphasis on whether their existing system can treat the spent cutting fluid before they even consider any other criteria like whether it may be the best cutting fluid for a given application [22]. Any great tribological advantages of a new cutting fluid would not even be considered if the existing cutting fluid disposal system cannot handle the disposal of this cutting fluid. Lucky exceptions are when even higher pressure exists to increase productivity, cost efficiency, quality, return on investment, etc., of metalworking operations. As such, however, the cutting fluid would be the last resort to implement after spending a fortune on new machines, cutting tools, Computer Aided Manufacturing (CAM) systems, expensive external consulting, etc. Corrosion resistance. The degree of corrosion resistance provided by a water-soluble cutting fluid is critical for protecting metal parts that are in touch with the fluid and thus should always be evaluated. Fluid corrosion tests are standardized in DIN 51 360. This test is actually the well-known Herbert test. Four small piles of clean steel chips are positioned on the cleaned and polished cast iron plate and are then whetted with the test mix. Four different dilutions of the same mix are used for four different chips. Plate and chips are placed in a closed container for 24 h, after which the formation of pits and staining is assessed. In critical application, a humidity chamber (ASTM D-1748) is used for testing corrosion resistance.

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Typically, an evaluation should be conducted in which various concentrations of cutting fluid delusions are rated for their degree of corrosion inhibition. The results are then evaluated by assessing the cutting fluid’s inhibition performance compared to other candidates, or by determining its acceptability in light of the user’s requirements, or according to both of these measures. Foam tendency. The forming tendency should always be evaluated if synthetic or semisynthetic cutting fluids are tested, particularly when the rate of cutting fluid flow is high as it is in gear hobbing and shaving, Baring-Trepanning Association (BTA) deep-hole drilling and boring, ring-gear, helical and pot broaching and high-production abrasive operations (as, for example, honing). Excessive foaming causes number of problems such as poor surface finish of the machined parts and reduced tool life. Foaming can also be caused by high cutting fluid concentration, mechanical problems as (crack in hose, too low sump level, crack in pump, too high pump pressure), soft water, high tramp oil content, etc. Foaming is also common in high-pressure cutting fluid applications. Most metalworking fluids contain surfactants and amines that are essentially soaps. Soft water combined with these soaps delivered to the cut zone under high pressure and shearing will tend to foam [66]. A variety of tests evaluating foaming have been developed, such as high-speed blender tests and forced aeration. The latter is standardized by ASTM D892-95. According to the procedure established by this standard, a defined volume of air is forced through a set volume of sample lubricant at a specified temperature. The resulting volume of foam is measured and an empirical rating of the foam tendency and the stability of the foam is determined. Generally, however, the foam height and the rates of foam decay should be compared with the user’s criteria and against the performance of other cutting fluid candidates. Health and safety. Evaluating the potential health hazards of a metalworking fluid is mandatory in today’s requirement [22]. The fluid supplier is normally the best source of information about a fluid. The supplier should be familiar with the health effects associated with the fluid to be used and can provide you with up to date material safety data sheets. Some suppliers go a step further and provide additional assistance such as providing a chemical or fluid management program, a customer support program and a product stewardship program which includes health, safety and environmental support. These programs can be especially helpful since they usually include current and comprehensive health and safety information required by Occupational Safety & Health Administration (OSHA)’s hazard communication standard, recommendations for effective fluid management, and information on the proper use and disposal of their products. The supplier may also be able to assure the user that his products comply with applicable governmental safety and environmental regulatory considerations; provide analysis of in-use fluids, including characterization of microbial content; and provide air sampling to measure employee exposure.

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The OSHA (US Department of Labor) made available an excellent document “Metal working fluids: Safety and Health. Best Practices Manual [67],” which was developed using the recommendations set forth in the OSHA Metalworking Fluids Standards Advisory Committee Final Report (1999); the NIOSH Criteria Document on Occupational Exposure to Metalworking Fluids (1998); and the Organization Resources Counselors, “Management of the Metal Removal Fluid Environment: A Guide to the Safe and Efficient Use of Metal Removal Fluids” (1999). Product stability. This property is not always considered by the user although it should be. An indication of neat material stability is helpful in determining the shelf life of the product under the storage conditions available in the manufacturing facility under consideration. Of greater importance is dilution stability. This property is related to the quality of water to be used in the metalworking coolant system. Especially hard water can cause performance deterioration with soluble, synthetic and semi-synthetic cutting fluids. Stability is tested using 24 h static stability or a longer term circulating stability test. In both the cases, observations are made for the degree of separation or precipitation that might occur at various dilutions. Long-term stability of soluble oils and semi-synthetic cutting fluids also includes bio-stability and emulsion stability over a wide range of water types with no scum formation. Another important aspect to assure cutting fluids stability is their compatibility with hydraulic fluids used by the user. The most common contaminant in cutting fluids is “tramp” oil. Tramp oil is formed when drops of lubricating oils, grease and hydraulic fluids fall from metalworking machinery into cutting fluids. It is also caused by oily, corrosion-protective coatings on workpieces. It is necessary for the intended users of lubricant, hydraulic oils and protective coatings that they do not use ordinary emulsifiers which dissolve in water. As a result, the droplets collect together as floating covers on the cutting fluid bath surface. This causes problems. Although not always, it is sometimes possible to buy lubricants, greases and cutting fluids that are chemically compatible. Suppliers can provide information on what materials work well together. Therefore, all these materials should be bought as an interacting system accounting for their chemical and physical compatibilities. Cost. Another important consideration in the selection process, naturally, is the unit cost of the cutting fluid. This cost should be calculated using some type of total cost analysis comparing the contending cutting fluids. The total cost should consist of at least two terms. The first is the spending part that includes all the expenses from sales price to disposal costs. The second part is the saving part that includes profit (if any) due to increased tool life, productivity, quality of the parts, etc. It is a good practice to keep a good record of the performance of current cutting fluid which then is used as a benchmark in the selection process. In trying to reduce the spending part, one should remember that the cutting fluid purchasing price is only about half a percentage of the total metal-working cost. Trying to reduce this cost by buying low-cost concentrate is not a good idea. Saving in concentrate

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cost will likely to be far outweighed by decreased productivity, reduced tool life, and increased cutting fluid maintenance and disposal costs. Buying cutting fluids from only one or two suppliers has a number of advantages. Loyal suppliers normally respond quickly when problems develop. This is particularly true if the users select suppliers that support their products. Supportive suppliers have their laboratory facilities that are equipped to measure the chemical and physical characteristics of cutting fluid. They also have application specialists capable of analyzing cutting fluid problems and recommending cost-effective solutions. A good cutting fluid supplier should make sure that the user’s metalworking operations are performing as efficiently as possible at the lowest overall cost. After fully evaluating all the data generated in the selection process, the most appropriate cutting fluid should emerge. If two or more cutting fluids still emerge favorably, their comparison is further carried out by external criteria. These criteria may include the vendor’s field service capability, shipping/delivery or even personal preference of the operator (color, odor, etc.). Upon completion of this thorough appraisal, the user will be in a good position to select the proper cutting fluid for improving his machining operation(s).

6.1.7 Generalizations In the author’s opinion, the researcher, cutting fluid developer and application specialists, and metal cutting practitioners should finally realize the following issues: • Although a simple and sound method to compare different cutting fluids for a particular machining operation would be beneficial and thus there have been a number of attempts made to develop such a method (for example, [35,62–64]), no suitable method has been developed for qualifying and comparing the performance of one cutting fluid with other [22,65] in terms of their influence on the cutting process. • Many manufacturing and plan managers are placing main emphasis on whether their existing system can treat the spent cutting fluid before they even consider any other criteria as to whether it may be the best cutting fluid for a given application [22]. Any great tribological advantages of a new cutting fluid would not be even considered if the existing cutting fluid disposal system cannot handle the disposal of this cutting fluid. Lucky exceptions are when even higher pressure exists to increase productivity, cost efficiency, quality, return on investment, etc. of metalworking operations. As such, however, the cutting fluid would be the last resort to implement after spending a fortune on new machines, cutting tools, CAM systems, expensive external consulting, etc. • Four basic mechanisms of cutting fluid access suggested in the literature on metal cutting, namely, access through capillarity network between chip and tool, access through voids connected with built-up edge formation, access into the gap created by tool vibration, propagation from the chip blackface through distorted lattice structure. The available theoretical and experimental data do not support any of these suggestions.

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• Although its use in metal cutting is proved to be successful in terms of improving tool life, reducing cutting forces and improving the integrity of machined surfaces, the cutting fluid does not penetrate the contact surfaces at the tool–chip and tool– workpiece interfaces. All the known “look-nice stories” about EP additives (chlorine and sulfur, for example) that prevent severity of the chip and workpiece contacts with the chip have no ground. • The major action of the cutting fluid is the embrittlement action that reduces the strain at facture of the work material. This action is based on the Rebinder effect [52]. Most of the effects formerly ascribed to EP lubricant action on the part of chorine, sulfur, and other boundary and EP types of fluids, are primarily due to strength reduction of the work metal during machining. The realization of the significance of this effect provides clear understanding why the application results of the same cutting fluid in “similar” work material, type of operation, machine, etc. can be considerably different. • Cooling action of cutting fluid is useful as far as it brings the cutting temperature closer to the optimal cutting temperature and as far as it brings the temperature of the workpiece to that suitable for the proper post-process handling (unloading, inspection, etc.). If, however, the cutting temperature due to the cooling action of the cutting fluid departures further from the optimal cutting temperature, the application of the cutting fluid reduces the tool life.

6.2 Coatings One of the most revolutionary changes in the metal cutting industry over the last 30 years is thin-film hard coatings and the thermal diffusion processes. These methods find everincreasing applications that brought significant advantages to their users. Today, 50% of HSS tool, 85% of carbide [68] and 40% of super-hard tools used in industry are coated. A great number of coating materials, methods and application regimes on the substrates or the whole tools, multi-layer coating combinations are used. This presents some confusion to the end users because: • A number of various coatings are recommended by multiple cutting inserts suppliers (manufacturers, cutting tool makers and distributors) for the same application. • Tool life varies considerably for the same coating material (or a combination of several materials for multi-layer coatings) produced by various carbide manufacturers or tool coating shops. It makes the selection of the coating materials difficult and confusing because the effectiveness of a particular coating material depends on a number of metallurgical regime and application factors hidden from the end user. The reported results and known discussions on the “goodness” of a particular coating material (or combination of materials and layer parameters) are very uncertain because this goodness is defined by a great number of other parameters, which are usually not reported. This section aims to introduce some very basic information about coatings used in the metal cutting industry and to provide end users with some information on the intelligent selection of the coated tool materials for a given application. It is not aimed to systematize

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existing coatings or discuss their application aspects because these are subjects for a separate book. In the author’s opinion, however, this book may become obsolete over the time of manuscript preparation and publishing because rapid development of new tool materials and various aspects of tool coating take place. Almost everyday carbide manufacturers come out with new coating materials, new regimes of their application, new substrate materials and new tool geometries, particularly topology of the cutting inserts (the sculptured shape of the rake face) more suitable for the coating they use.

6.2.1 Choice of coating materials and coating processes Ideally, the simple and straightforward objective of the application of any particular coating is to improve the tribological conditions at the tool–chip and tool–workpiece interfaces. It can be realized in practice, however, if these conditions are known and, what is even better, can be controlled. When it is not feasible, the predominant tool wear mechanism (discussed in Chapter 3) should be identified and the suitable coating capable of reducing the severity of this type of wear should be selected. Sometimes, it is more feasible to change the contact conditions that change the predominant tool wear mechanism. For example, when diffusion is identified as the predominant tool wear mechanism, a coating that reduces contact friction (for a given work material) and thus the temperature at the interface considered can be used because diffusion occurs only at high contact temperatures. A great attempt to correlate the coating materials and their performance was made [69]. It was pointed out that basically, there are four major groups of coating materials in the market. The most popular group is titanium-based coating materials like TiN, TiC and Ti(C,N). The metallic phase is often supplemented by other metals like Al and Cr, which are added to improve some particular properties like hardness, oxidation resistance, etc. The second group represents ceramic-type coatings like Al2 O3 (aluminum oxide) coatings. The third group includes super-hard coatings like CVD diamond, and the fourth group includes solid lubricant coating such as amorphous metal-carbon. Additionally, to reduce extensive tool wear during runoff period, some soft coatings like MoS2 or pure graphite are deposited on the top of hard coatings.

6.2.2 Application techniques Coatings are applied by three basic types of techniques: • Chemical vapor deposition (CVD) involves a chemical reaction between a gaseous phase (e.g. titanium and nitrogen) and the surface of a substrate (a cutting insert or cutting tool) heated to approximately 1000◦ C. Because CVD coating is a gaseous process, all the surfaces of the substrate may be uniformly coated. • Physical vapor deposition (PVD), in which the metal component of the coating is produced from solid, in a high vacuum environment. The generation of the metal atoms is accomplished by evaporation or ion bombardment methods, at temperatures of approximately 500◦ C.

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• Thermal diffusion (TD) is applied in a molten borax bath, with the addition of vanadium, at approximately 1000◦ C. The resultant vanadium carbide coating has very good results in numerous applications. • Dynamic compound deposition (DCD) coating process (developed by Richter Precision Co.) is a proprietary low-temperature coating process that synthesized dry-film lubricant and wear-resistant coating components. CVD coatings have been commercially available for about 30 years, and the fact that more than half of the inserts sold are CVD coated testifies to the effectiveness of these coatings. CVD coatings usually are deposited in multi-layer composition. A TiC–TiN multi-layer, for instance, provides the lubricity of TiN and the abrasion resistance of TiC. Coating thickness is in the range of 5–10 µm. However, the high temperatures (about 1000◦ C) involved in the CVD process create an embrittlement called “eta phase” at the coating–substrate interface. Depending on its extent, the embrittlement can affect the operational performance involving interruptions of cut and inconsistency of workpiece microstructure such as the one found in some nodular irons. Recently developed medium temperature CVD (MTCVD) coatings have shown a reduced tendency to the formation of eta phase. MTCVD-coated tools offer increased resistance to thermal shock and edge chipping compared to the conventional CVD-coated tools. The result is greater tool life as well as increased toughness compared to high-temperature CVD coatings [70]. PVD coatings also offer advantages over CVD coatings in certain operations and/or workpiece materials. Commercialized in the mid-1980s, the PVD coating process involves relatively low deposition temperatures (approximately 500◦ C), and permits coating of sharp insert edges (CVD-coated insert edges are usually honed before coating to minimize the effect of eta phase.). Sharp and strong insert edges are essential in operations such as broaching, gear shaving, milling, drilling, threading and cutoff and for effective cutting of the so-called “long-chip” materials such as low-carbon steels. In fact, a wide range of “problem” materials – such as titanium, nickel-based high alloys and nonferrous materials – can be productively machined with PVD-coated tools. From a workpiece structure point of view, sharp edges reduce cutting forces, so PVD-coated tools can offer a true advantage when machining thin-wall components or when the machining residual stresses are the issue. The first PVD coatings were titanium nitride (TiN), but more recently developed PVD technologies include titanium carbonitride (TiCN) and titanium aluminum nitride (TiAlN), which offer higher hardness, increased toughness and improved wear resistance. TiAlN tools in particular, through their higher chemical stability, offer increased resistance to chemical wear and thereby increased capability for higher speeds. Recent developments in PVD coatings include “soft” coatings such as molybdenum disulfide (MoS2 ) for dry drilling applications. Soft–hard coating combination such as MoS2 over a PVD TiN or TiAlN, also demonstrated great potential, as the hard (TiN or TiAlN) coating provides wear resistance while the softer, more lubricious outer layer expedites chip flow [70–72]. The basic PVD coatings are listed in Table 6.8 and their properties are shown in Table 6.9. Effectiveness of various coatings on cermet cutting tools is discussed in [73,74].

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Table 6.8. Basic PVD coatings. Titanium nitride (TiN)

Titanium carbonitride (TiN(C,N))

Titanium aluminum nitride ((Ti,Al)N)

Chromium nitride (CrN)

Multi-layer CrN–CrC Multi-layer TiN–TiCN

Zirconium nitride (ZrN) TiN–TiCN–TiC–Al2 O3 TiN–TiCN–TiC–Al2 O3 –TiN TiN–TiCN–Al2 O3 –TiN

The gold-colored TiN coating offers excellent wear resistance with a wide range of materials, and allows the use of higher feeds and speeds. Forming operations can expect a decrease in galling and welding of workpiece material with a corresponding improvement in surface finish of the parts formed. A conservative estimate of tool life increase is 200–300%, although some applications see as high as 800%. Bronze-colored Ti(C,N) coating offers improved wear resistance with abrasive, adhesive or difficult-to-machine materials, such as cast iron, high alloys, tool steels, copper and its alloys, Inconel and titanium alloys. As with TiN, feeds and speeds can be increased and tool life can improve by as much as 800%. Forming operations with abrasive materials should see improvements beyond those experienced with TiN. Purple/black in color, (Ti,Al)N is a high-performance coating which excels at machining of abrasive and difficult-to-machine materials such as cast iron, aluminum alloys, tool steels and nickel alloys. (Ti,Al)N’s improved ductility makes it an excellent choice for interrupted operations, while its superior oxidation resistance provides unparalleled performance in high-temperature machining. Silver in color, CrN offers high thermal stability, which in turn helps in aluminum die casting and deep draw applications. It can also reduce edge build-up commonly associated with machining titanium alloys with Ti-based coatings. Silver in color, the coating has good hardness and a high resistance to cracking and chipping. It is suitable for machining Al and Ti alloys. Bronze/gray or blue/gray in color, the coating is recommended for tough machining applications as machining of high-carbon steels, tool steels and high silicon aluminum alloys. Pale gold in color, this general purpose coating is recommended for machining of cast irons and non-ferrous materials as Al and Ti alloys. Black colored, this coating has high thermal and oxidation resistance. Gold colored, the coating is suitable for milling and turning roughing applications. Gold colored, the coating is characterized by wear resistance in milling and turning.

DCD is based on the principle of in situ mechanical activation and chemical transformation, and leads to considerably decreased friction and increased durability of the coated products. Due to the specific conditions of synthesis, DCD coatings develop micro- and macro-structures that are well adapted for conditions like severe contact loading. For this reason, DCD coatings are primarily suited for high sliding speeds and contact pressure applications.

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Tribology of Metal Cutting Table 6.9. Basic physical properties of PVD coatings.

Property

Color Hardness (HV) Coating thickness (µm) Thermal stability in (◦ C) (◦ F) Lubricity TiN/steel Deposition temperature in (◦ C) (◦ F) Cost comparison

Titanium nitride Titanium Titanium Chromium nitride (TiN) carbonitride aluminum nitride (CrN) (Ti(C,N)) ((Ti,Al)N) Gold 2800 2–4

Bronze 3000 2–4

Purple/black 2800 2–4

Silver 2000–2200 3–5

550 1000 0.4–0.55

400 750 0.5–0.6

750 1350 0.5–0.6

800 1470 0.55–0.65

500 930 Base

500 930 1.5 × base

500 930 2 × base

350 660 1.75 × base

6.2.3 Selection notes It should be pointed out, however, that a great variety of coatings available in the market makes the selection of the most suitable one for a particular application very cumbersome. The trial-and-error method is widely used in such a selection simply because the coating properties (such as residual stress, topology, morphology, hardness, thermal conductivity, coating substrate adhesion, resistance to abrasion, resistance to tribooxidation, resistance to adhesion, etc.) are poorly correlated with cutting conditions. In the author’s opinion, there is nothing wrong with the listed characteristics itself. The problem is in known methods and regimes used in their determination (listed in Ref. [75]). Unfortunately, the existing methods and regime used do not resemble the tribological conditions found at the tool–chip and tool–workpiece interfaces in terms of stresses and their distributions, temperature distributions, velocities, etc. The situation is somewhat similar to that for the cutting fluids described earlier in this chapter. As a result, there could be many controversial opinions on the same coating used in “similar” applications (sometimes it works very well; sometimes it does not help at all) because no criterion (criteria) of tribological similarity is used. It is instructive to point out the following: • A specific coating would be beneficial if and only if it is properly used. If this is the case, tool life of the coated tool increases 2–3 times compared to that of the uncoated tool. Moreover, increases of 10–50% in productivity have been demonstrated in some applications. • Typically coatings will not solve tooling problems and thus efforts in this direction are fruitless. In other words, the selection of proper cutting tool and machining regime for the cutting operation should be accomplished as a prerequisite for coating applications. • Coating usually adds 0.6–1 µm of surface roughness. Post-coat polishing is possible; however, no data on this process is available [70].

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• Coating does change the dimensions of the cutting tool. Change depends on the coating, its specified thickness and the coating process. Typically, PVD is recommended for high-tolerance tools and CVD for loose tolerance tools. Most PVD coatings add 2–3 µm per side to a tool or component. CVD and PVD CrN are thicker and can add 10 µm or more in some cases. Processing temperatures may grow or shrink some substrate materials. CVD temperatures, in particular, affect the heat treatment conditions of tools and components and can cause dimensional changes. • Coatings are often applied in multiple alternating layers. This is because the hardness increases as its grain size decreases, and the grain size decreases simultaneously with the decrease in coating thickness [76]. This is especially true for alumina coatings; thinner alumina coating layer are harder. Harder coatings provide better wear resistance. The desirable maximum thickness: minimum grain size was not attainable before the introduction of alternating multi-layer coating [76]. The most common method of achieving the reduction of grain size in Al2 O3 layers is to periodically interrupt their deposition by applying a thin layer of TiC, TiCN or TiN. Growth of grains inhibited in each succeeding Al2 O3 layer. The application of more layers in this way can be used to build up to the desired overall coating thickness while keeping grain growth in Al2 O3 layers to a minimum. • The effectiveness of various coatings depends on the type of machining operation and machining regime. In low-speed end milling, wear resistance is determined by the presence of chromium in the coating while at high-speed end milling TiAlN coatings assures high wear resistance. In turning, the effectiveness of different coatings depends on the cutting speed, as shown in Fig. 6.17. • The best results are achieved when multi-layer coatings like (TiAl)N, (AlTi)N and (AlTiCr)N coatings are used. Their use: (a) reduces the strength of adhesion bonds at

T(min)

60 1

2 40

3 4

20 5 0 100

200

300

400

n(m/min)

Fig. 6.17. Influence of cutting speed on tool life for cutting inserts with various coatings. Longitudinal turning, no cutting fluid. Work material: AISI steel 4140, HB200, cutting feed f = 0.26 mm/rev, depth of cut dw = 3 mm. Tool geometry: cutting edge angle κr = 60◦ , normal flank angle αn = 7.5◦ , normal rake angle γn = −7.5◦ Substrate – carbide M30. Coatings: (1) TiCrN, (2) AlTiN, (3) no coating, (4) TiN and (5) TiCrN.

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Tribology of Metal Cutting the tool–chip interface and thus reduces the severity of the friction at this interface, (b) improves tool life; (c) increases machining superficial and in-depth residual stresses because greater portion of the thermal energy generated in machining flows into the workpiece [77].

In recent years, new diamond coatings were developed for machining nonmetallic or nonferrous work materials. Earlier, polycrystalline diamond (PCD) tools and “hard” carbide grades were used for this purpose. Now, a variety of carbon-based cutting tool coatings are available. They are termed CVD diamond, diamond-like carbon (DLC), amorphous diamond, hard carbon and a host of brand name designations. In reality, these coatings can be grouped into three generic categories: true diamond, DLC and hard carbon. Basic properties of DLC are listed in Table 6.10. Amorphous (a-C) and hydrogenated amorphous carbon (a-C:H) films have high hardness, low friction, electrical insulation, chemical inertness, optical transparency, biological compatibility, ability to absorb photons selectively, smoothness and resistance to wear. For a number of years, these economically and technologically attractive properties have drawn almost unparalleled interest towards these coatings. Carbon films with very high hardness, high resistivity and dielectric optical properties, are now described as diamond-like carbon or DLC [78]. Several methods have been developed for producing diamond-like carbon films: 1. Primary ion beam deposition of carbon ions (IBD). 2. Sputter deposition of carbon with or without bombardment by an intense flux of ions (physical vapor deposition (PVD)). 3. Deposition from an RF plasma, sustained in hydrocarbon gases, onto substrates negatively biased (plasma-assisted chemical vapor deposition (PACVD)). Until recently, the work on DLC worldwide has not yielded the expected benefits in the field of wear resistance and general mechanical performance. Most of the success has Table 6.10. Some basic properties of diamond and DLC materials. Property

Thin film CVD diamond

Bulk a-C

a-C:H

Diamond

Form Faceted crystals Smooth or rough Smooth Faceted crystals Hardness (HV) 3000–12 000 1200–3000 900–3000 7000–10 000 2.8–3.5 1.6–2.2 1.2–2.6 3.51 Density (g/cm3 ) Refractive index – 1.5–3.1 1.6–3.1 2.42 > 1010 106 –1014 > 1016 > 1013 Electrical resistivity (Ω/cm3 ) Thermal 1100 – – 2000 conductivity (W/m◦ K) Chemical stability Inert Inert Inert Inert

Graphite

2.26 2.15 0.4 3500 Inert

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been in applications for magnetic storage media and optical coatings. The reasons for this are: • only thin coatings (<1 µm) have been used, • the 2D aspect of most of the deposition routes, • the difficulty in gaining good adhesion to metallic substrates. One of the main problems with DLC deposition at low temperature is the creation of very high internal stress levels in the films. This, combined with the ensuing lattice mismatch when DLC is applied to a wide range of substrates, commonly leads to poor adhesion. In high mechanical stress applications, the adhesion of the films is of paramount importance. This problem has now been overcome by ensuring that there are no stress concentrations near the coating–substrate interface. The magnetron sources are used to deposit a series of multi-layer compounds prior to the deposition of DLC. The layers have graded interfaces. This ensures that there are no abrupt changes in composition, and that the stress is introduced into the film gradually. The optimum multi-layer structure series is: titanium, titanium nitride, titanium carbonitride, titanium carbide and then the DLC. It has also been subsequently found that the mechanical properties of the hard carbon films can be improved by incorporating a small percentage of metal dopant (usually ∼ 5% titanium) in the final carbon structure. The resulting films have excellent friction and wear properties: • microhardness of up to 4000 HV, • coefficient of friction during dry running in air against cemented WC Tungsten– Cobalt alloys < 0.15, • wear rate 20% of that of titanium nitride, • exceedingly low counterface wear. The application of DLC coating on cutting tools resulted in significant improvement in tool life in some applications and allowed dry cutting in some applications. However, the major problem is a great scatter in tool life results, although the mean tool life is higher than that with TiN-coated tools. This is because the DSL film lacks adhesion to the cutting tool surface so it is peeled off at early stage of the cutting process and thus the tool could not utilize the discussed advantages of the DSL film. Recently, some research teams found different ways to increase the adhesion properties of DSL coatings [79].

6.3 Improving Tribological Conditions by Modification of Properties of the Work Material In the author’s opinion, one of the major hidden resource in improving tribological conditions in metal cutting (reduced tool wear and improved quality of the machined surface), and thus reducing the cost per unit of the machined part is in the properties and structure of the work material. Unfortunately, this simple and self-obvious resource

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did not prevent sufficient attention of researchers and practitioners in the field of metal machining although the properties of the work material define to a large extent: • Properties of the chip contact surface which is the counterpart of the tool rake face over the tool–chip contact length. • Properties of the work material at the tool–workpiece interface (the flank surface), which define the contact conditions and tool wear over this interface. It is interesting to point out that the properties of the tool materials and coating at the discussed interfaces are subjects of a great body of theoretical and experimental studies from the shop floor level (for example [80,81]) to high level of applied physics (for example [82–84]), while among the properties and conditions of the work material in many studies in the field, only generic (not actual) chemical composition (or AISI (SAE, ASM) designation like AISI steel 1045, for example), hardness and material dealer state (for example, as rolled, annealed, hot rolled, cold rolled, extruded etc.) are mentioned. In the author’s experience, these are not sufficient even to the first approximation to characterize the machinability of the work material and thus the contact processes at the tool–chip and tool–workpiece interfaces. As a result, a great scatter in experimental data is a nuisance in experimental metal cutting. When it comes to industry, one expects that high costs of poor machinability, great scatter in tool life (that particularly hurts in production-automated lines and manufacturing cells with no or minimum human attendance) and great scrap rate prevented at least some attention of practical manufacturing engineers to the properties of the work material. Unfortunately, this is not the case even in the most advanced industries and manufacturing facilities. This is particularly true in the automotive industry where the losses due to misunderstanding and/or underestimation of the discussed issue result in the losses of tens of millions of dollars. In the author’s experience, the hidden loses are even greater than that as a number of premature failures of powertrain components (first of all, transmissions) are due to the burr and chips left after machining. Manufacturers have been reluctant to hold the materials suppliers to a narrow range of chemical composition and hardness variation in the materials supplied. The variations in the chemical composition and hardness make it very difficult to specify the optimum tool geometry, suitable grade of the tool material and optimal machining regime. Moreover, it is next to impossible to implement the results of tribological studies under these conditions as the modeled and experimentally obtained data cannot be relevant for the whole range of properties of the work materials. Some common causes for poor material specification in manufacturing and research practices are: • Prime cause is the lack of knowledge and readily available data on the correlation of the properties (both mechanical and metallurgical) of work material and their machinability (not to mention the metal cutting tribology). • False perception that tighter specifications and control of metallurgical properties would always result in higher cost of blanks (casting, forgings etc.) and materials. There are two major misunderstandings: (a) often, the tightened specification reduces the usage of some very expensive materials, for example in gray

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cast iron; requirements to increase the hardness of gray cast iron lead to reduced annealing time that, in turn, reduces the energy (natural gas or electricity) spent, (b) the automotive industry rapidly shifts from the consideration of the cost of individual components (blanks, tool, parts, etc.) to that of the cost per unit including reliability of the processes and the final products. In such a context, even if the cost of blanks or raw materials grows, the overall saving on the much higher tool and process costs, process stability, chip disposal, better quality of the machined part and assembly structures would be many hundred times than this increased cost. • Many automotive companies have developed standards on material specification more than 20 years ago, so these standards do not reflect the advances made in the materials production and control. To change any particular specification is a cumbersome process that requires persistence and consumes a lot of time of the originator. Moreover, since the automotive industry has outsourced the tooling management, this originator – the tooling application specialist – is an outsider that makes this task even more difficult. When it comes to research and development, the following causes can be listed: • Prime cause is the lack of knowledge on the relevant properties of the work material relevant to metal cutting in general and to the metal cutting tribology in particular. The known books and articles on machinability of materials (for example [5,85]) are of a little help in such understanding. • High cost of metallographic equipment. Many universities and research laboratories cannot afford to have the equipment needed. Unfortunately, in the application of equipment grants for metal cutting studies, metallographic equipment is not considered as needed by many grant committees. • Difficulties in altering the metallurgical and mechanical properties of the work material. The objective of this section is to present two simple examples showing that the machinability of the work material and thus the tribological conditions at the interfaces and, as a result, tool wear (tool life) can be significantly improved via controlling the metallurgical state of the work material.

6.3.1 Heat treatment Heat treatment regime of many work materials alters their microstructural characteristics and physical properties so it affects tool wear and thus the tribological process at the tribological interfaces. Among many pre-process heat treatment used today, isothermal annealing is the most widely used process. The practice of annealing which results in transformation at a constant temperature is referred to as isothermal annealing in contrast to continuous cooling annealing, where transformation to ferrite and pearlite takes place over wide range of temperatures. This also produces full annealing structure for the purpose of: (a) inducing softness, (b) producing definite microstructure, (c) altering mechanical properties and (d) removing stresses. Although it is also believed that

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isothermal annealing improves the machinability of materials [86], the known literature sources did not provide any specific quantitative information on improved machinability due to annealing. To clarify the issue and to show the influence of the regime of isothermal annealing on tool wear, Talantov conducted a series of machining tests [87]. Forgings made of AISI steel 4320 were subjected to 10 different industry regimes of isothermal annealing. The forgings selected for the control batch were normalized at a standard temperature of 935◦ C. The tests were carried out using accelerated cutting regime: cutting speed ν = 1.5 m/s, cutting feed f = 0.815 mm/rev. Tool material was P20 (75% WC, 5% TiC, 10% Co), tool geometry was: rake angle γn = 0◦ , major flank angle αn = 10◦ , minor flank angle αn1 = 10◦ , tool cutting edge angle κr = 45◦ , tool minor cutting edge angle κr1 = 45◦ and inclination angle λp = 0◦ . The tool life criteria was the average width of the flank wear VBB = 0.4 mm. The experimental results showed that tool life differs significantly depending upon a particular regime of isothermal annealing. Two regimes of this annealing were selected for further detailed study: AN1 which results in the poorest tool life and AN2 which results in the greatest tool life. The results obtained for the normalized work material (N) were used as a reference as this heat treatment process is widely used in practice as a premachining heat treatment. Figure 6.18 shows wear curves for the said heat treatments. As seen, the difference is so significant that it cannot be just ignored in the research and practice of metal cutting. The next step was to determine the root cause of the discussed difference in tool wear. It was suggested that this cause lays in the differences in the deformation properties of the two solid phases found in the work material used, namely, ferrite and pearlite. To verify this suggestion, the partially formed chips obtained using a quick-stop device were subjected to a metallographic study. These chips were sectioned from the rest of the workpiece, mounted, ground, polished and etched to obtain specimens that can then be

VBB(min) AN1

N

AN2

0.4 0.3 0.2 0.1

0

1

2

3

4

5

6

Fig. 6.18. Wear curves.

7

8

tct (min)

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KHV kHV−f

0.5

kHV−p kHV−f

kHV−f

0.4 0.3

kHV−p

0.2 kHV−p 0.1 0 N

AN2

AN1

Fig. 6.19. Hardening coefficients for ferrite (kHV −f ) and pearlite (kHV −p ) solid phases.

viewed microscopically. The difference in the deformation properties of the phases was assessed by the level of strain hardening of the phases. To do this, the microhardness (load 0.05 N) of the ferrite and pearlite phases was measured in the above-mentioned specimens. Using the average microhardness data, the hardening coefficient kHV was determined for ferrite (kHV −f ) and pearlite (kHV −p ) phases as kHV = HV 1 −

HV , HV 1

(6.48)

where HV and HV 1 are the microhardnesses of a phase before and after machining, respectively. The results shown in Fig. 6.19 suggest that the reason for good machinability achieved in the annealing AN2 is approximately equal strain hardening of the two discussed solid phases in the workpiece structure. A further metallographic study showed that the reason for reduced wear is the increase in the actual contact area at the tool–chip and tool– workpiece interfaces as in the case of AN2 as both the solid phases bear the contact load so the contact stresses become much lower.

6.3.2 Influence of grain size Another way to reduce the severity of the contact conditions at the tool–chip and tool– workpiece interfaces is to create a fine-grain structure with uniform distribution of small flakes of hard cementite (Fe3 C). A perception was that smaller and evenly distributed hard inclusions should reduce the severity of the contact conditions at the tool–chip and tool–workpiece interfaces. To verify it experimentally, Talantov [87] carried out a series

384

Tribology of Metal Cutting

of cutting tests. The following conditions were used in the tests: work material – three steel grades, namely, AISI 1045, 1020 and 1070. Tool material – P20 (85% WC, 5% TiC, 10% Co). Cutting feed f = 0.4 mm/rev, depth of cut dw = 1.5 mm. Tool geometry: rake angle γn = 0◦ , major flank angle αn = 10◦ , minor flank angle αn1 = 10◦ , tool cutting edge angle κr = 45◦ , tool minor cutting edge angle κr1 = 45◦ and inclination angle λp = 0◦ . The tool life criteria was the average width of the flank wear VBB = 0.4 mm. The first series of tests included a comparison of tool lives for the two batches of workpieces made of AISI steel 1045 having different grain size. The first batch was heat treated so that it had the flaked pearlite metallurgical structure while the second – tempered sorbite. To make a relevant comparison, both the structures were brought to the same hardness HB 1800 MPa. The microhardness of the chip contact area was measured at the middle of the tool–chip contact length (the end of the zone of plastic contact). To do that, the specimens of the partially formed chip were produced using a quick-stop device during actual machining at a cutting speed of 1 m/s. These chips were sectioned from the rest of the specimens, mounted, ground, polished and then subjected to microhardness tests. The test results revealed that microhardness of the chip contact layer was HV = 5800 MPa for the flaked pearlite metallurgical structure, while it was HV = 4800 MPa for the micrograin tempered sorbite structure. To explain the phenomenon, the chip contact layers were studied using scanning electron microscopy. It was found that there is almost no ferrite at the chip contact surface for the flaked pearlite metallurgical structure while both the solid phases (ferrite and pearlite) in approximately equal proportion were found for the micrograin tempered sorbite structure. The result obtained is readily explained by the fact that a micrograin structure prevented the independent deformation of the solid phases and thus squeezing the pearlite phase into the contact surface. Moreover, cementate was distributed much more evenly in this structure. As a result, the hardness of the contact layer is smaller for this case. As anticipated, the revealed difference in the microhardness of the chip contact layer affect other tribological characteristics of the cutting process: • For the same cutting speed (ν = 1 m/s), the cutting temperature was measured to be 940◦ C in machining of the work material having the flaked pearlite metallurgical structure, while this temperature was only 895◦ C for the work material having micrograin tempered sorbite structure. • Tool life was found to be 1.42–2.10-fold greater for the work material having micrograin tempered sorbite structure, as shown in Fig. 6.20. • Cutting force was found to be 25–30% smaller (depending on the cutting speed and feed) for the work material having micrograin tempered sorbite structure. The tests with AISI steels 1020 and 1070 did not show the same dependence. It was explained by the fact that both the steels have only one predominant solid phase, namely 1020 – ferrite, 1070 – pearlite so that the tribological conditions in machining these steels do not depend on their grain size.

Improvements of Tribological Conditions

385

T (min) 120 1

n=0.83m/s

2 80

n=1.70m/s

1 40 2 0

1800

2200

HB (MPa)

Fig. 6.20. Influence of hardness of AISI steel 1045 on tool life for the workpiece having (1) tempered sorbite and (2) flaked pearlite structures, at two different speeds.

6.3.3 Influence of minor elements in work materials Normally, the influence of alloy additions on mechanical and physical properties, corrosion and chemical behavior, and processing and manufacturing characteristics are considered by mechanical and physical metallurgy. Normally, the coverage considers “alloying” to include any addition of an element or compound that interacts with a base metal to influence the properties. The prime consideration addresses the beneficial effects of major alloy additions, inoculants, dopants, grain refiners and other elements that have been deliberately added to improve the performance of alloys [88]. Although the detrimental effects of minor elements or residual (tramp) elements included in the charge materials or that result from improper melting or refining techniques are discussed, such discussions are of qualitative nature and primarily relates to the mechanical and physical properties. It is a common practice in the automotive industry to add some minor alloying elements and elements traces to improve the castability, formability, heat treatment properties or some minor working properties of the parts concerned, for example crankshafts. Unfortunately, possible changes in the machinability of various modified work materials (castings, forgings, bar stocks etc.) are not considered as important. This is because, there are very few studies that relate the influence of minor alloying components and components in traces on machinability so many tool manufacturing processes and quality specialists are not aware about the strength of the correlation discussed. As a result, wide range of variations of these components is allowed by common specification of materials used in the automotive industry. When the allowed range is changed or minor component is added to the specification of a material by part designers, the manufacturing and process specialists may not be informed about this change.

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A good example of the influence of minor components on the machinability of gray cast iron, widely used in the automotive industry, was presented by Griffin and co-workers [89]. They found that within the range allowed for manganese (0.3–0.8%), the longest tool life corresponds to 0.3% and it reduces by more than twice when the content of manganese is 0.8%. The same result was obtained for the allowable range of tin. Even more pronounced influence of volume percent of hard inclusion was found in this study. Unfortunately, the conclusive results obtained did not affect the methodology used by the automotive industry in specifying composition of gray, ductile and malleable cast irons although significant cost saving can be achieved with minimum efforts. Moreover, quality and reliability of cars can be improved by the reduction in the number of defective transmissions and engine due to metallic chips and burrs left in weans and gates of case body, pump cover, upper and lower valve bodies, etc.

References [1] Grzesik, W., Advanced Protective Coatings for Manufacturing and Engineering, HanserGardner Publications, Cincinnati, OH, 2003. [2] Holmberg, K., Mathews, A., Coatings Tribology: Properties, Techniques and Applications in Surface Engineering, Elsevier Science, London, 1994. [3] Bunshah, R.F., ed., Handbook of Hard Coatings: Deposition Technologies, Properties and Applications, William Andrew Publishing, New York, 2001. [4] Shaffer, W.R., Cutting tool edge preparation, SME Paper TP99PUD68, 2000. [5] Mills, B., Redford, A.H., Machinability of Engineering Materials, Applied Science Publishers, London, 1983. [6] Fang, X.D., Zhang, D., An investigation of adhering layer formation during tool wear progression in turning of free-cutting stainless steel Wear, 197 (1996), 169–178. [7] Qi, H.S., Mills, B., Formation of a transfer layer at the tool-chip interface during machining, Wear, 245 (2000), 136–147. [8] Kumabe, J., Vibration Cutting, Jikkyo Publisher, Tokyo, 1979. [9] Taylor, F.W., On the art of cutting metals, Transactions of ASME, 28 (1907), 70–350. [10] Childers, J.C., The chemistry of metalworking fluids, in Metalworking Fluids, J.P. Byers, Editor. Marcel Dekker, New York, 1994, pp. 165–189. [11] Mariani, G., The selection and use of semi-synthetic coolants, SME Paper MF90-321, 1990, pp. 1–10. [12] Graham, D., Dry out, Cutting Tool Engineering, 52 (2000), 1–8. [13] Brinksmeier, E., Walter, A., Janssen, R., Diersen, P., Aspects of cooling application reduction in machining advanced materials, Proceedings of the Institution of Mechanical Engineers, 213 (1999), 769–778. [14] Nasir, A., General comments on ecological and dry machining. In Network Proceedings “Technical Solutions to Decrease Consumption of Cutting Fluids,” Sobotin-Sumperk, Czech Republic, 1998, pp. 10–14.

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[15] Machado, A.R., Wallbank, J., The effect of extremely low lubricant volumes in machining, Wear, 210 (1997), 76–82. [16] Sreejith, P.S., Ngoi, B.K.A., Dry machining: machining of the future, Journal of Materials Processing Technology, 101 (2000), 287–291. [17] Brinksmeier, E., Walter, A., Janssen, R., Diersen, P., Aspects of cooling application reduction in machining advanced materials, Proceedings of the Institution of Mechanical Engineers, 213 (1999), 769–778. [18] Cutting Fluid Management: Small Machining Operations, Third Edition. Iowa Waste Reduction Center, University of Northern Iowa, 2003. http://www.iwrc.org/downloads/ pdf/cuttingFluid03.pdf [19] De Chiffre, L., Function of cutting fluids in machining, Lubrication Engineering, 44 (1988), 514–518. [20] Chen, N.N.S., Pun, W.K., Stresses at the cutting tool wear land, International Journal of Machine Tools and Manufacture, 28 (1988), 79–92. [21] Bailey, J.A., Friction in metal machining – mechanical aspect, Wear, 31 (1975), 243–253. [22] Smolenski, D.J., Standards for fluids take time, Manufacturing Engineering, 134 (2005), 149–157. [23] Metalworking Fluid Magazine, Metalworking fluid selection, http://www.metalworkingfluid. com/?page=selection.htm. [24] Byers, J.P., Laboratory evaluation of metalworking fluids, in Metalworking Fluids, J.P. Byers, Editor. Marcel Dekker, New York, 1994, pp. 191–221. [25] Zorev, N.N., ed. Metal Cutting Mechanics, Pergamon Press, Oxford, 1966. [26] Atkins, A.G., Modelling metal cutting using modern ductile fracture mechanics: qualitative explanations for some longstanding problems, International Journal of Mechanical Science, 45 (2003), 373–396. [27] Russell, W.R., Cutting tools for cutting fluid evaluation, Lubrication Engineering, 30 252–254, 1978. [28] Williams, J.A., Tabor, D., The role of lubricants in machining, Wear, 43 (1977), 275–292. [29] Williams, J.A., The action of lubricants in metal cutting, Journal of Mechanical Engineering Science, 19 (1977), 202–212. [30] Kronenberg, M., Machining Science and Application. Theory and Practice for Operation and Development of Machining Processes, Pergamon Press, Oxford, 1966. [31] Talantov, N.V., Unstable plastic deformation and self-exited vibrations in metal cutting (in Russian), in Metalworking Technology and Automatization of Manufacturing Processes, N.V. Talantov, Editor. VPI, Volgograd, 1984, pp. 37–41. [32] Astakhov, V.P., Metal Cutting Mechanics, CRC Press, Boca Raton, US, 1998. [33] Talantov, N.V., Physical Fundamentals of the Metal Cutting Process and Tool Wear (in Russian), VolPI, Volgograd, Russia, 1988. [34] Iyengar, H.S.R., Salmon, R., Rice, W.B., Some effects of cutting fluids on chip formation in metal cutting, ASME Journal of Engineering for Industry, 87 (1965), 36–38.

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[35] Medaska, M.K., Nowag, L., Liang, S.Y., Simultaneous measurement of the thermal and tribological effects of cutting fluid, Machining Science and Technology, 3 (1999), 425–432. [36] Shaw, M.C., Metal Cutting Principles, Oxford Science Publications, Oxford, 1984. [37] Epifanov, G.I., Rebinder, P.A., Energy balance of the metal cutting process (in Russian), Doclady Academii Nauk (Henry Brutcher Translation No. 2394), 66 (1949), 653–656. [38] Smart, E.F., Trent, E.M., Coolants and cutting tool temperatures, in Improving Production with Coolants and Lubricants, E. Zintak, Editor. SME, Dearborn, MI, 1982, pp. 8–16. [39] Lienhard IV, J.H., Lienhard, V.J.H., A Heat Transfer Textbook, Third Edition. Phlogiston Press, Lexington, MA, 2003. [40] Holman, J.P., Heat Transfer, McGraw-Hill, New York, 2001. [41] Seah, K.H.W., Li, X., Lee, K.S., The effect of applying coolant on tool wear in metal machining, Journal of Material Processing Technology, 48 (1995), 495–501. [42] Li, X., Study of the jet-flow rate of cooling in machining. Part 1. Theoretical analysis, Journal of Materials Processing Technology, 62 (1996), 149–156. [43] Mazurkiewicz, M., Kubala, Z., Chow, J., Metal machining with high-pressure water-jet cooling assistance – a new possibility, ASME Journal of Engineering for Industry, 111 (1989), 7–12. [44] Entelis, S.G., Berlinder, E.M., Cooling-Lubricating Media for Metal Cutting (in Russian), Machinostroenie, Moscow, 1986. [45] Crafoord, R., Kaminski, J., Lagerberg, S., Ljungkrona, O., Wretland, A., Chip control in tube turning using a high-pressure water jet, Proceedings of the Institution of Mechanical Engineers Part B, 213 (1999), 761–767. [46] Reznikov, A.N., Reznikov, L.A., Thermal Processes in Machining Systems (in Russian), Machinostroenie, Moscow, 1990. [47] Chiou, R.Y., Chen, J.S.J., Lu, L., North, M.T., The effect of an embeded heat pipe in a cutting tool on temperature and wear. In ASME International Mechanical Engineering Congress and Exposition, ASME, Washington, DC, November 15–21, 2003. [48] Judd, R.L., Aftab, K., Elbestawi, M.A., An Investigation of the use of heat pipes for machine tool spindle bearing cooling, International Journal of Machine Tools and Manufacture, 34 (1994), 1131–1143. [49] Peterson, G.P., Chapter 12 – Heat pipes, in Handbook of Heat Transfer, Third edition, J.P.H.W.M. Rohnsenow, Y.I. Cho, Editors. McGraw-Hill, Washington, DC, 1999. [50] Faghri, A., Heat Pipe Science and Technology, Taylor and Francis, Washington, DC, 1995. [51] Rebinder, P.A., Surface Effects in Dispersion Systems (in Russian), Nauka, Moscow, 1979. [52] Epifanov, G.I., Solid State Physics (in Russian), Vysjaya Shcola, Moscow, 1977. [53] Griffith, A.A., The phenomena of rupture and flow in solids, Philosophical Transactions, Series A, 221 (1921), 163–198. [54] Wojciechowski, F.K., Theory of chemisorption on metal surfaces, The Proceedings of the Physical Society, 87 (1966), 583–585.

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[55] Norsko, J.K., Chemisorption on metal surfaces, Reports on Progress in Physics, 53 (1990), 1253–1295. [56] Springborn, R.K., Cutting and Grinding Fluids: Selection and Application, SME, Dearborn, MI, 1967. [57] Hong, S.Y., Ding, Y., Cooling approaches and cutting temperatures in cryogenic machining of Ti-6Al-4V, International Journal of Machine Tools and Manufacture, 41 (2001), 1417–1437. [58] Wang, X.Y., Rajurkar, K.P., Cryogenic machining of hard-to-cut materials, Wear, 239 (2000), 168–175. [59] Zurecki, Z., Harruott, G., Zhang, X., Dry machining of metals with liquid nitrogen, SME Paper MR99-252, 1999, pp. 1–12. [60] Hong, S.Y., Ding, Y., Ekkens, G., Improving low carbon steel chip breakability by cryogenic chip cooling, International Journal of Machine Tools and Manufacture, 39 (1999), 1065–1085. [61] De Chiffre, L., Mechanical testing and selection of cutting fluids, Lubrication Engineering, 36 (1980), 29–33. [62] Colwell, L.V., A method for studying the behavior of cutting fluids in wear of tool materials, Transaction ASME, 80 (1958), 1054–1059. [63] de Chiffre, L., Testing the overall performance of cutting fluids, Lubrication Engineering, 34 (1978), 244–251. [64] Itava, K., Uoda, K., The significance of dynamic crack behavior in chip formation, Annals of the CIRP, 25 (1976), 65–70. [65] Aronson, R.B., Using high-pressure fluids. Cooling and chip removal are critical, SME Manufacturing Engineering, 132(6) (2004), 34–46. [66] US Department of Labor, METALWORKING FLUIDS: Safety and Health, Best Practices Manual. US Department of Labor, 1999. [67] Astakhov, V.P., Tribology of metal cutting, in Mechanical Tribology, H.L.G.E. Totten, Editor. Marcel Dekker, New York, 2004, pp. 307–346. [68] Klocke, F., Krieg, T., Coated tools for metal cutting – features and applications, Annals of the CIRP, 48 (1999), 515–525. [69] Arnold, D.B., Trends that drive cutting tool development. Metalworking Technology Guide 2000, in Modern Machine Shop online, 2000. [70] Segal, L., Tovbin, R., Hard coatings for heavy duty stamping tools, SAE Paper Number 1999–01-3230, 1999. [71] Srivastava, A.K., Quinto, D.T., Experimental investigations into turning of Aermet 100 alloy using uncoated and TiAIN coated inserts, ASME Paper TP05PUB97, 2005, p. 10. [72] Bushman, B., Gupta, B.K., Handbook of Tribology – Materials, Coatings, and Surface Treatments, McGraw-Hill, New York, 1991. [73] Leep, H.R., Metal cutting processes, in Metalworking Fluids, J. Byers, Editor. Marcel Dekker, New York, 1994, pp. 61–98.

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[74] McCabe, M.J., Advances in PVD and CVD thin film wear resistant coatings, SME Paper MR97-229, 1997, pp. 1–14. [75] Bradford, S.L., Battaglia, F.B., Alumina coated grades in high speed machining, SME Paper FC90-248, 1990, pp. 1–10. [76] Outeiro, J.C., Dias, A.M., Lebrun, J.L., Astakhov, V.P., Machining residual stresses in AISI 316L steel and their correlation with the cutting parameters, Machining Science and Technology, 6 (2002), 251–270. [77] Monaghan, D.P., Laing, K.C., Logan, P.A., Teer, P., Teer, D.G., Diamond-like carbon coatings, Materials World, 1 (1993), 347–349. [78] Kagiya, Y., Tsuda, K., Fukui, H., Iyori, H., Yamagata, K., Development of DLC coating film (AURORACOAT) and its application to tools, SEI Technical review, 56 (2003), 89–94. [79] Saletri, R.A., Sisler, D.E, Cutting tool geometries: a user perspective, SME Paper MR92-360, 1992, pp. 1–10. [80] Ezugwu, E.O., Key improvements in the machining of difficult-to-cut aerospace superalloys, International Journal of Machine Tools and Manufacture, 40 (2005), 1353–1367. [81] Qi, Y., Hector, L.G., Hydrogen effect on adhesion and adhesive transfer at aluminum/diamond interfaces, Physical Review B, 68 (2003), 201403-201401–201403-201404. [82] Qi, Y., Hector, L.G., Adhesion and adhesive transfer at aluminum/diamond interfaces: a first-principles study, Physical Review B, 69 (2004), 235401-235401–235401-235413. [83] Qi, Y., Hector, L.G., Oot, N., Adams, J.B., A first principles study of adhesion and adhesive transfer at AL(111)/graphite(0001), Surface Engineering, 581 (2005), 155–168. [84] Rao, R.V., Gandhi, O.P., Digraph and matrix methods for the machinability evaluation of work materials, International Journal of Machine Tools and Manufacture, 42 (2002), 321–330. [85] Harmer, S., Heat Treatment of Steels – The Processes, Azom.com jn-line article, (2004), [86] Talantov, N.V., Physical Fundamentals of the Cutting Process, Tool Wear and Failure (in Russian), Machinostroenie, Moscow, 1992. [87] Davis, J.R., ed. Alloying: Understanding the Basics, ASM, Metal Park, OH, 2001. [88] Griffin, R.D., Li, H.J., Elftheriou, E., Bates, C.E., Machinability of gray cast iron, AFS Transactions, 01-159 (2002), 1–17.

APPENDIX A

Basics, Definitions and Cutting Tool Geometry

To implement the results of any study on the tribology of metal cutting in the right direction, one should clearly understand the geometry of the cutting tool used. A proper understanding of cutting tool geometry enables one to determine the orientation of the cutting edge, rake and flank surfaces with respect to the cutting velocity, so that the actual rake, flank and inclination angles can be found for any given point of the cutting edge(s). Despite the existence of national and ISO standards on tool geometry, the current level of understanding of the subject provides no systematic guidance to enable quick homing-in on the right solution(s). The existing text and reference books on the subject do not provide sufficient support in the identification of the static geometry parameters even for simple single-point cutting tools. As no information can be found on the actual uncut chip parameters one wonders how to apply the theory of metal cutting to calculate the cutting parameters (cutting force, tool wear, surface specifications of the machined parts, etc.) for a given tool geometry. Although ISO “Basic Quantities in Cutting and Grinding – Part1: Geometry of the Active Part of Cutting Tools – General Terms, Reference Systems, Tool and Working Angles, Chip Breakers” (ISO 3002) provides some information on the subject, it is still insufficient for a clear understanding of the cutting tool geometry. The problem is that the existing theories and thus the tribomodels of metal cutting usually consider free orthogonal cutting and their conclusions are valid for this case. In practice, however, one always deals with non-free non-orthogonal cutting and thus a clear way to apply the results of metal cutting theories properly should be developed. One of the mandatory steps for this is a clear understanding of the tool geometry. A1 Basic Terms and Definitions The geometry and nomenclature of cutting tools, even single-point cutting tools, are surprisingly complicated subjects [1]. It is difficult, for example, to determine the appropriate 391

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Tribology of Metal Cutting

planes in which the various angles of a single-point cutting tool should be measured; it is especially difficult to determine the slope of the tool face. The simplest cutting operation is one in which a straight-edged tool moves with a constant velocity in a direction perpendicular to the cutting edge of the tool. This is known as the two-dimensional or orthogonal cutting process illustrated in Fig. A1(a). The cutting operation can be best understood in terms of orthogonal cutting parameters. Figure A1(b) shows the application of a single-point cutting tool in a turning operation. It helps to correlate the orthogonal and oblique non-free cutting. The basic definitions of the terms involved are as follows:

A1.1 Workpiece surfaces In orthogonal cutting (Fig. A1(a)), the two basic surfaces of the workpiece are considered: • Work surface is the surface of the workpiece to be removed by machining. • Machined surface is the surface produced after the cutting tool pass. In many practical machining operations additional surface is considered: • Transient surface is the surface being cut by the major cutting edge (Fig. A1(b)). By comparing Figs. A1(a) and A1(b), one should realize that the cutting edge in orthogonal cutting forms the machined surface while in oblique non-free cutting this surface is formed by the so-called tool nose and by the minor cutting edge (discussed later).

A1.2 Tool surfaces and elements • Rake face is the surface over which the chip formed in the cutting process slides. • Flank face is the surface(s) over which the surface produced on the workpiece passes. • Cutting edge is a theoretical line of intersection of the rake and the flank faces. • Cutting wedge is the tool body enclosed between the rake and the flank faces. • Shank is the part of the tool by which it is held.

A1.3 Types of cutting Orthogonal cutting is a type of cutting where the straight cutting edge of the wedgeshaped cutting tool is at right angles to the direction of cutting, as shown in Fig. A1(a). Besides, the additional distinctive features of the orthogonal cutting are: (a) the cutting edge is wider than the width of cut, (b) no side spread of the layer being removed occurs after its transformation into the chip, (c) plane strain condition is the case, i.e. a single

Basics, Definitions and Cutting Tool Geometry

Rake face

Direction of prime motion (Cutting direction)

Rake angle, g

Chip width

393

Tool Machined surface Chip

Width (depth) of cut (Uncut chip width)

t2

dw1

Flank face

Work surface Flank (Relief) angle, a

dw

Cutting wedge Cutting edge Chip thickness

t1

Thickness of the layer being removed (Uncut chip thickness)

Workpiece

(a) Work surface

Transient surface Machined surface

Direction of prime (speed) motion

Workpiece

Chip

Direction of feed motion

Tool

(b) Fig. A1. Visualization of basic terms: (a) orthogonal cutting and (b) turning.

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Tribology of Metal Cutting

“slice” (by a plane perpendicular to the cutting edge) of the model shown in Fig. A1(a) can be considered in the analysis of the chip formation model. This type of cutting, however, is characterized by a 3D state of stress and (d) the cutting edge does not pass the previously machined surface by this cutting edge, so that there is no influence of the previous cutting passes on the current cutting pass. This is not the case in tube end turning, which is often used to simulate orthogonal cutting, because the temperatures and machining residual stresses built on the previous pass might significantly affect the cutting conditions on the current pass. Moreover, this influence depends on many cutting parameters like the rotational speed of the tubular workpiece (which defines the time difference between the two successive positions of the cutting edge and the intensity of the residual heat), axial feed (which defines the machining residual stresses leave that the previous pass of the cutting tool) etc. In the author’s opinion, this makes the end-tube turning unsuitable for simulating orthogonal cutting [1]. Oblique cutting is a type of cutting where the straight cutting edge of the wedge-shaped cutting tool is not at right angles to the direction of cutting. Free cutting is a type of orthogonal or oblique cutting when only one cutting edge is engaged in cutting. Non-free cutting is a type of cutting where more than one cutting edge is engaged in cutting so that the chip flows from the engaged cutting edges interact with each other. A2 Reference Planes The cutting tool geometry includes a number of angles measured in different planes. Figure A2 visualizes the definition of the main reference plane Pr as perpendicular

z

2 3

1

vf y 2'

kr 1

Main Reference Plane

Pr

kr

3' 1'

vf

x

Fig. A2. Definitions of the reference plane Pr and tool cutting edge angles κr and κr1 .

Basics, Definitions and Cutting Tool Geometry

395

to the assumed direction of primary motion (the z direction in Fig. A2). This figure also sets the tool-in-hand coordinate system. In this figure, νf is the assumed direction of the cutting feed, line 1–2 is the major cutting edge and line 1–3 is the minor cutting edge. Because angles of the cutting tool are defined in a series of reference planes, the standard system defines a system of these planes in the tool-in-hand system, as shown in Fig. A3. The system consists of five basic planes defined in relation to the reference plane Pr : • Perpendicular to the reference plane Pr and containing the assumed direction of feed motion is the assumed working plane Pf . • The tool cutting edge plane Ps is perpendicular to Pr , and contains the major cutting edge (1–2 in Fig. A2). A proper analysis of the cutting tool geometry is important to understand that: (a) if the major cutting edge is a straight line then the tool cutting edge plane is the same for any point of this edge. This plane is fully defined by two intersecting lines, namely, by the straight cutting edge and the vector of the cutting speed; (b) if the major cutting edge is not straight, there are infinite number of tool cutting edge planes. As such, a tool cutting edge plane has to be defined for each point of the curved cutting edge as the plane which is tangent to the cutting edge at the point of consideration and which contains the vector of the cutting speed (or perpendicular to the main reference plane).

Cutting edge plane Back plane

Orthogonal plane

Assumed working plane

z

Pp Ps vf

Po Pf Pfi

Pn Cutting edge normal plane

Pr

Fig. A3. Standard system of reference planes.

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Tribology of Metal Cutting

• The tool back plane Pp is perpendicular to Pr and Pf . • Perpendicular to the projection of the cutting edge into the reference plane is the orthogonal plane Po . When the cutting edge is not straight, there are infinite number of orthogonal planes defined for each and every point of the curved cutting edge. For a given point of the curved cutting edge, the cutting edge of the orthogonal plane is defined as the plane which is perpendicular to the tangent to the projection of the cutting edge into the reference plane edge at the point of consideration. • The cutting edge normal plane Pn is perpendicular to the cutting edge. When the cutting edge is not straight, there are infinite number of cutting edge normal planes defined for each and every point of the curved cutting edge. For a given point of the curved cutting edge, the cutting edge normal plane is defined as the plane perpendicular to the tangent to the cutting edge at the point of consideration.

A3 Angles: Definitions The geometry of a cutting element is defined by certain basic tool angles and thus precise definitions of these angles are essential. A system of tool angles is shown in Fig. A4 and is known as the tool-in-hand system [1]. Rake, wedge and flank angles are specified by γ, β and α, respectively, and these are identified by the subscript of the plane of intersection. The definitions of basic tool angles in the tool-in-hand system are as follows: • ψr is the tool approach angle; it is an acute angle that Ps makes with Pp and is measured in the reference plane Pr , as shown in Fig. A4. • The rake angles are defined in the corresponding planes of measurement. The rake angle is the angle between the reference plane (the trace of which in the plane of measurement considered appears as the normal to the direction of primary motion) and the intersection line formed by the plane of measurement considered and the tool rake plane. The rake angle is defined as being acute and positive always when looking across the rake face from the selected point and along the line of intersection of the face and the plane of measurement. The line of intersection viewed lies on the opposite side of the tool reference plane from the direction of primary motion in the measurement plane for γf , γp and γo or a major component of it appears in the normal plane for γn . The sign of the rake angles is well defined (Fig. A4). • The flank angles are defined in a way similar to the rake angles, though the line of intersection viewed here lies on the opposite side of the cutting edge plane Ps from the direction of feed motion, assumed, or actual as the case may be, then the flank angle is positive. Angles αf , αp , αo and αn are clearly defined in the corresponding planes, as shown in Fig. A4. The flank (clearance) angle is the angle between the tool cutting edge plane Ps and the intersection line formed by the tool-flank plane and the plane of measurement considered, as shown in Fig. A4. • The wedge angles βf , βp , βo and βn are defined in the planes of measurements. It is the angle between the two intersection lines formed as the corresponding plane of measurement intersects with the rake and flank planes. For all the cases, the sum

Basics, Definitions and Cutting Tool Geometry

397

Pr

gf

SECTION F−F (Plane Pf ) Pp

SECTION O−O (Plane PO )

bf SECTION O'−O' (Plane O')

Ps

af

Pr

−g

ao

go

O' S

a1o F

bo

P

O

1 0

3

F

+g SECTION P−P (Plane Pp )

Pf

kr 1 ap

kr 2 yr O'

an

O

bp

SECTION N−N (Plane P )n

bn gp P r

P

Ps

N

gn

N VIEW S

ls

+l Pr

(Plane P )s

−l

Fig. A4. Tool angles in the tool-in-hand system.

of rake, wedge and clearance angles is 90◦ , i.e. γp + βp + αp = γn + βn + αn = γo + βo + αo = γf + βf + αf = 90◦

(A1)

• The orientation and inclination of the cutting edge are specified in the tool cutting edge plane Ps . In this plane, the cutting edge inclination angle λs is the angle between the cutting edge and the reference plane. This angle is defined as always being acute and positive if the cutting edge, when viewed in a direction away from the selected point at the tool corner being considered, lies on the opposite side of the reference plane from the direction of primary motion. This angle can be defined at any point of the cutting edge. The sign of the inclination angle is well defined in Fig. A4. • The definition of the tool cutting edge angle κr is shown in Fig. A2. It is defined as the acute angle that the tool cutting edge plane makes with the working plane

398

Tribology of Metal Cutting assumed and is measured in the reference plane Pr . It can also be defined as the acute angle between the projection of the main cutting edge into the reference plane and the x direction. Angle κr is always positive and it is measured in a counter-clockwise direction from the position of the working plane assumed.

• Similarly, the tool minor (end) cutting edge angle κr1 is the acute angle that the minor cutting edge plane makes with the working plane assumed and is measured in the reference plane Pr . It can also be defined as the acute angle between the projection of the minor (end) cutting edge into the reference plane and the x direction (Fig. A4). Angle κr1 is always positive (including zero) and it is measured in a clockwise direction from the position of the working plane assumed.

A3.1 Cutting edge angle The tool cutting edge angle significantly affects the cutting process because, for a given feed and cutting depth, it defines the uncut chip thickness, width of cut, and thus tool life. The physical background of this phenomenon can be explained as follows: when κr decreases, the chip width increases correspondingly because the active part of the cutting edge increases. The latter results in improved heat removal from the tool and hence the tool life increases. For example, if the tool life of a High Speed Steel (HSS) face milling tool having κr = 60◦ is taken to be 100%, when κr = 30◦ , its tool life is 190%, and when κr = 10◦ its tool life is 650%. Even more profound effect of κr is observed in the machining with single-point cutting tools. For example, in rough turning of carbon steels, the change of κr from 45 to 30◦ sometimes leads to a fivefold increase in the tool life. The reduction of κr , however, has its drawbacks. One of them is the corresponding increase of the radial component, (Fy ) of the cutting force. Figure A5(a) shows that in general, the cutting force, (R) is a 3D vector and thus it can be resolved into three orthogonal components, namely, the power (tangential, torque) component (Fz ) (often referred to in literature on metal cutting as (FT ), axial component (Fx ) and radial component (Fy ). For simplicity, these are often called tangential, axial and radial forces, respectively. As shown in Fig. A5(b), the radial and axial forces are related as Fx = tan κr Fy

(A2)

From Eq. (A2), lowering κr from 45 to 20◦ results in more than twofold increase in the radial force that increases the bending force acting on the workpiece and thus may reduce the accuracy of machining because the rigidity of the workpiece varies along its length. When the workpiece is machined between the centers, an increased radial force causes the so-called barreling, and when the workpiece is clamped only in the chuck, tapering may occur. Besides, since lowering κr leads to an increased radial force, this force often causes vibrations so that the advantages of small cutting edge angle may not become too profound.

Basics, Definitions and Cutting Tool Geometry

z

399

y

Rxy Fy

Fx

x

Fx

x

kr1

Fy kr R

y

kr Rxy

Fz

(a)

(b)

f

dw

kr 1

kr b1

(c) a1

Fig. A5. The cutting force system and the uncut chip thickness for a single-point cutting tool.

Another drawback of small κr is the reduction in the uncut chip thickness t1 . From Fig. A5(c) t1 = f sin κr ,

(A3)

where f is the cutting feed per revolution. It follows from Eq. (A3) that under a given feed f, the uncut chip thickness can be varied in a wide range by changing the angle κr . When this angle becomes zero, the uncut chip thickness is also zero (no cutting) and when κr = 90◦ , the uncut chip thickness reaches its maximum becoming t1 = f as in orthogonal cutting. Hence, t1 ∈ (0, f ). The following equation for the uncut chip area correlates the feed (f ) and the depth of cut (dw ) with the uncut chip thickness (t1 ) and non-orthogonal chip width dw1 = b1 dw f = t1 dw1 = Aw

(A4)

and t1 = f sin κr

(A5)

dw , sin κr

(A6)

dw1 =

where Aw is the cross-sectional area of the uncut chip.

400

Tribology of Metal Cutting

From Eq. (A4), under a given feed and depth of cut, any change of t1 causes a corresponding change of dw1 = b1 . As shown, when t1 ∈ (0, f ), the chip width dw1 ∈ (∞, dw ). In general, the specific cutting force (the force that is acting on the unit length of the cutting edge) is proportional to the uncut chip thickness. For this reason, the uncut chip thickness is often referred to as the chip load in literature on metal cutting. As discussed earlier in this book, this parameter is of great importance in determining many tribological characteristics of the cutting process. A rule of thumb here is: the smaller the chip load, the higher the tool life, and vice versa. However, there is the minimum uncut chip thickness (under other given cutting parameters) below which the opposite effect is true. Two factors primarily limit the minimum allowable uncut chip thickness: • Decreasing the uncut chip thickness, one should increase the width of cut according to Eq. (A4). When t1 → 0, dw1 → ∞, i.e. the length of the cutting edge should be increased to infinity. Obviously, this is not practical. • Uncut chip thickness cannot be less than the radius of the cutting edge. Real cutting cannot be regarded as free cutting because real tools always have more than one cutting edge engaged in cutting. There have been a number of attempts to allow for the inter-influence of the neighboring cutting edges in determining the direction of chip flow. They are well summarized in [2]. Klushin [3] and Stabler [4] suggested the determination of the true uncut chip thickness t1T in a plane perpendicular to the direction of chip flow while the true uncut chip width b1T (dw1T ) in the perpendicular direction and equal to the length of the segment AB, which joins the ends of the major and minor cutting edges engaged in cutting, as shown in Fig. A6. In this figure, the directions AC and BC are orthogonal chip flow directions of the major and minor cutting edges, respectively, and the direction AB is the resultant chip-flow direction. The angle between AC and AB is referred to as the chip-flow angle ηch . The segment AB is often referred

C B hch BC

AC

A AB

Fig. A6. Chip-flow direction.

Basics, Definitions and Cutting Tool Geometry

f

401

f

rn

rn dw dw

kr 1

kr

kr 1

kr

kr

kr 1

O

(a)

(b) 1.1f

f

dw

kr

kr 1

dw

kr

(c)

(d)

Fig. A7. Four basic configurations in non-free cutting.

to as the equivalent cutting edge, as suggested by Colwell [5]. Therefore, in non-free cutting, the uncut chip thickness depends on the orientation of the equivalent cutting edge. Figure A7 presents four basic configurations in non-free cutting. The first configuration, shown in Fig. A7(a), represents the most common single-point tools in use today. The cutting tool is made with a nose radius rn and set so that the depth of cut is greater than the nose radius. If the following relationships are justified dw ≥ rn (1 − cos κr ),

f ≤ 2rn sin κr1

(A7)

then the formulas for calculation of t1T and b1T are as follows: t1T =

f c1 sin arctan [1 − e1 (1 − cos κr )] cot κr + e1 (sin κr + g1 ) c1

(A8)

b1T =

c 1 dw , sin arctan {c1 /([1 − e1 (1 − cos κr )] cot κr + e1 (sin κr + g1 ))}

(A9)

where

 c1 = 1 − e1 1 − 1 − g1 ,

e1 =

rn , t1

g1 =

f 2rn

(A10)

402

Tribology of Metal Cutting

The second configuration, shown in Fig. A7(b) is similar to the first except that only the radius part of the cutting edge is engaged in cutting. If the following relationships are justified dw < rn (1 − cos κr ) ,

f ≤ 2rn sin κr1

(A11)

the formulas for calculation of t1T and b1T are as follows: t1T =

f c1 sin arctan √ c1 2e1 − 1 + e1 g1

(A12)

b1T =

c 1 dw   √ sin arctan c1 /(e1 g1 + 2e1 − 1)

(A13)

In the third configuration (Fig. A7(c)), the nose radius is rather small compared to the depth of cut, so that only the straight parts of the major and minor cutting edges are considered. Then the formulas for calculation of t1T and b1T are as follows: t1T =

f q1 sin arctan q1 1 + cot κr − q1

(A14)

b1T =



c 1 dw , √ sin arctan c1 /(e1 g1 + 2e1 − 1)

(A15)

1 f dw cot κr + cot κr1

(A16)

where q1 = 1 −

In the fourth configuration (Fig. A7(d)), the nose radius is rather small so that only the straight parts of the major and minor cutting edges are considered. To improve the machined surface finish, the minor cutting edge is positioned parallel to the axis of rotation of the workpiece so that κr1 = 0. As such, the length of the minor cutting edge is usually selected to be equal to 1.1f . The formulas for calculation of t1T and b1T are as follows: t1T = f sin arctan b1T =

1 cot κr + 2.2e1 g1

dw sin arctan (1/(cot κr + 2.2e1 g1 ))

(A17) (A18)

Although the fourth configuration has been known for many years and its advantages are well documented, its implementation has often been accompanied by vibration and thus was restricted by the rigidity of the machine tools. Only recently, when machine tools became rigid enough, it became possible to use tools with such geometry on rigid milling machines. Cutting inserts of such geometry known now as wiper inserts are widely used in practice.

Basics, Definitions and Cutting Tool Geometry

403

In operation, “wiper” technology is designed to improve surface finishes in milling applications. It works by positioning an insert with a flat, just-below-the-other ordinary parallel land inserts on a face mill. As the “wiper” passes through the cut, it smoothens the surface. It allows using much higher feed rate without compromising surface finish of the machined areas. Example 1 Problem: Find the uncut chip area for the major and minor cutting edges (assuming κr1 = 0◦ ) when feed f = 0.3 mm/rev, depth of cut dw = 2 mm for tools having the cutting edge angle κr = 45◦ and κr = 85◦. Solution: Using Eq. (A4), we can calculate the uncut chip area of the major cutting edge for the first and second tools because the depth of cut and the cutting feed are the same for both the tools Aw = f × dw = 0.3 × 2 = 0.6 mm2 Using Eq. (A25), we can calculate the maximum uncut chip area for the minor cutting edge For the first tool Awm = 0.5f 2 tan κr = 0.5 × 0.32 tan 45◦ = 0.045 mm2 For the second tool Awm = 0.5f 2 tan κr = 0.5 × 0.32 tan 85◦ = 0.515 mm2 As shown, the uncut chip area for the minor cutting edge for the second tool is almost the same as that for the major cutting edge. Therefore, the cutting forces generated due to the minor cutting edge cannot be ignored because the cross-sectional area of the uncut chip for this edge is almost the same like the major cutting edge. Moreover, since this edge is not meant to cut any significant amount of the work material, its cutting geometry (the rake and the flank angles) are not selected to perform efficient cutting, so the cutting forces generated by this edge are normally much higher than those generated by the major cutting edge under the same conditions. The problem gets worsened when the depth of cut decreases. A3.2 Rake angle Rake angles are three types, positive, zero (sometimes referred to as neutral) and negative, as shown in Figs. A8(a)–(c), respectively. It is generally accepted that the increase in the rake angle reduces the horsepower consumption per unit volume of the layer being removed as 1% per degree starting from γ = −20◦ . As a result, the cutting force and tool–chip contact temperature change in approximately the same way. So, it seems to be reasonable to select a high positive rake angle for practical cutting operations. Everyday

404

Tribology of Metal Cutting

Workpiece

f Tool g = 0° −g +g

(a)

(b)

(c)

Fig. A8. (a) Positive, (b) zero and (c) negative rake angles.

machining practice, however, shows that there are number of drawbacks in increasing the rake angle. The main drawback is that the strength of the cutting wedge decreases when the rake angle increases. The reason for that is illustrated in Fig. A9. When cutting with a positive rake angle, as shown in Fig. A9(a), the interaction of the tool rake face with the moving chip results in certain distributions of the normal and tangential stresses over the contact length lc . As discussed in Chapter 3, these distributions can be represented in terms of the corresponding resultant normal N and tangential F forces acting on the cutting wedge. As shown, the normal force N causes the bending of the tip of the cutting wedge. The presence of bending significantly reduces the strength of the cutting wedge causing its chipping. Moreover, the tool–chip contact area reduces with the rake angle, so the point of application of the normal force shifts closer to the cutting edge. On the contrary, when cutting with a tool having a negative rake angle (Fig. A9(b)), the normal force N acting on the tool rake face does not cause the bending mentioned. Instead, it results in the compression of the tool material. Because hard tool materials have very high compressive strength, the strength of the cutting edge in this case is much higher although the normal force N is greater than that for tool with positive rake angles. This is particularly true when superhard tool materials (for example, Poly-Crystalline Diamond (PCD) and Cubic Boron Nitride (CBN)) are used in interrupted and hard turning. It has to be mentioned, however, that rapid development of PCD and CBN materials led to their increased bending strength, so tools with positive geometries are used in machining of high-silicon aluminum alloys in the automotive industry even in interrupted cutting operations. Another important drawback is that the region of the maximum contact temperature at the tool–chip interface shifts toward the cutting edge when the rake angle is increased, which lowers the tool life, as discussed in Chapter 3.

Basics, Definitions and Cutting Tool Geometry

smax

Cutting direction

Chip

405

Normal contact stress

N

tmax

Tangential contact stress

F m Tool

lc

lc

(a) smax Cutting direction

N

tmax

F

lc

lc

(b) Fig. A9. Forces acting on the cutting edge having: (a) positive rake angle and (b) negative rake angle.

Realistically, the rake angle is not an independent variable in the tool geometry selection process because the effect of rake angle depends upon other parameters of the cutting tool geometry and the cutting process. Moreover, the necessity of applying chip breakers of different shapes often dictates the resulting rake angle rather than other parameters of the cutting process like tool life, power consumption and cutting force.

A3.3 Flank angle If the Flank (relief) angle α = 0◦ , then the flank surface of the cutting tool is in full contact with the workpiece. As such, due to spring-back of the workpiece material, there is significant friction force in such a contact that leads usually to tool breakage. The flank angle affects the performance of the cutting tool mainly through decreasing the rubbing on the tool’s flank surfaces. When the uncut chip thickness is small (less than 0.02 mm), this angle should be in the range of 30–35◦ to achieve maximum tool life. The flank angle directly affects the tool life. When angle α increases, wedge angle β decreases, as shown from Fig. A4. As such, the strength of the region adjacent to the cutting edge decreases as well as heat dissipates through the tool. These factors lower the tool life. On the other hand, by increasing the flank angle the following advantages are obtained:

406

Tribology of Metal Cutting

T

t1−2 Tool Life

t1−1 t1−2 > t1−1

VB

8°

a1

a2

Flank Angle

30°

(a)

α

(b)

Fig. A10. Influence of flank angle: (a) the difference in the worn tool materials under the same flank wear for different flank angles and (b) on tool life.

The cutting edge radius decreases with the flank angle that leads to corresponding decrease in the frictional and deformation components of the flank force. This effect becomes noticeable in cutting with small feeds. As a result, less heat is generated that leads to an increase in tool life. As the flank angle becomes larger, more tool material should be removed (worn out) to reach the same flank wear as shown in Fig. A10(a). As a result, the tool life increases. Due to such contradictive effects, the influence of flank angle on tool life always has a well-defined maximum, as shown in Fig. A10(b). One has to remember the most important rule in assigning the flank angle which reads: “The actual flank angle should not be less than 3◦ ” (exceptions are some form of tools such as broaching tools, gear hobs and shapers, shaving tools, etc.). Otherwise the normal cutting operation can be hardly performed due to vibrations and excessive tool wear. Therefore, it is very important to estimate the actual flank angle(s) accounting for the tool design, its installation in a machine, its working conditions including the direction of the prime and feed motions. One should also remember that in machining difficult-to-machine materials, a 2◦ change in the flank angle might change the tool life by twice. The same can be said about the integrity of machined surfaces. If the actual flank angle is close to 0◦ or negative, the interference of the tool flank surface and the workpiece takes place, i.e. the tool profile runs into the workpiece profile. In the theory of profile generation by cutting tools, the interference of the first, second and third

Basics, Definitions and Cutting Tool Geometry

407

kind as well as local and global interference are considered. The interference mentioned can result in interference mark on the tool body, at the best, or it leads to rapid tool damage and makes the cutting operation impossible.

A3.4 Cutting edge radius As discussed above, the tool designer apparently has the rake and the flank angle design parameters to optimize the tool performance. Practice of tool production, however, proves that this is not always the case. The problem is that the edge is assumed to be very sharp compared to the thickness of the layer to be removed and, therefore, the actual rake angle is the same as that assigned by the tool drawing. This is true for more than 80% of the metalworking operations, where the thickness of the layer to be removed is 10–20-fold greater than the radius of the cutting edge. As such, this radius is simply neglected and the cutting tool is considered to be perfectly sharp. Unfortunately, the same cannot be applied to many finishing and hard turning operations with a very “light” uncut chip thickness. One may wonder: what seems to be the problem? To understand the problem, consider the model of cutting shown in Fig. 3.46 (Chapter 3), where a cutting tool having a radius of the cutting edge ρce is shown. The tool is set to remove the uncut chip thickness t1 . Due to the radius of the cutting edge, this uncut chip thickness is divided into two parts: the actual uncut chip thickness ta , which is removed by cutting and thus turns into the chip, and the deformed uncut chip thickness h1 which is ploughed under the tool. When the ratio t1 /ρ1 ≥ 10, the effect of ρ1 is small so the tool is considered to be perfectly sharp. However, when t1 /ρ1 < 10, the relative impact due to ploughing by the rounded cutting edge becomes significant and thus cannot be ignored. Naturally, the cutting process ceases at certain t1 /ρ1 turning to be pure burnishing or ploughing. It is discussed in Chapter 3 that the cutting process ceases and the layer to be removed undergoes plastic deformation similar to burnishing when (Eq. (3.69)) h1 τin ≤ 0.5 − , ρce σy

(A19)

where σy is the yield strength of the work material and τin is the shear strength of adhesion bonds between work and tool materials. The shear strength of adhesion bonds primarily depends on the mechanical properties of the work material and the contact temperature. Equation (A19) allows us to determine the limiting uncut chip thickness (t1−lim = h1 ) for a given combination of work and tool materials. However, one should note that the cutting process becomes unstable even before this limiting value is reached. It can be easily detected by excessive vibrations, poor surface finish and reduced tool life.

408

Tribology of Metal Cutting

Example 2 Problem: Determine the minimum feed that can be used in the machining of 303 stainless steel with the depth of cut t1 = 2 mm by a carbide insert KC850 (Kennametal) having the cutting edge angle κr = 72◦ , nose radius r1 = 0.8 mm and cutting edge radius ρce = 0.055 mm. Solution: For the steel considered τin = 145 MPa and σy = 264 MPa. From Eq. (A19), the limiting uncut chip thickness is calculated as     τin 145 = 0.055 0.5 − = 0.025 mm t1−lim = ρce 0.5 − σy 264 Given conditions indicate that we deal with the case shown in Fig. A7(a). Therefore, we can calculate the critical cutting feed using iteration method for Eq. (A8) fcr = t1−lim c1

1 sin arctan (c1 / ([1 − e1 (1 − cos κr )] cot κr + e1 (sin κr + g1 ))) 1

= 0.025 × c1 sin arctan

, c1 [1 − 0.4(1 − cos 72)] cot 72 + 0.4(sin 72 + g1 )

where fcr fcr rn 0.8 = = , e1 = = 0.4 and 2rn 2 × 0.8 t1 2



  c1 = 1 − e1 1 − 1 − g1 = 1 − 0.4 1 − 1 − g1 .

g1 =

The minimum cutting feed fcr = 0.039 mm/rev was calculated using MathCAD. To verify that the case considered corresponds to Fig. A7(a), we can check the conditions set by Eq. (A7)   t1 = 2 ≥ rn (1 − cos κr ) = 0.8 1 − cos 72◦ = 0.55 : valid fcr = 0.039 ≤ 2rn sin κr1 = 2 × 0.8 × sin 72 = 1.52 : valid A3.5 Inclination angle Although the sense and sign of the inclination angle λs is clearly shown in Fig. A4 and it is defined earlier as the angle between the cutting edge and the reference plane, experience shows that there are certain difficulties and confusions in understanding this angle. Figure A11 aims to clarify the issue. The inclination angle λs is measured in a plane H which is perpendicular to the reference plane xy and passes through the tool tip

Basics, Definitions and Cutting Tool Geometry

409

z y

1

2

ls = 0°

+ls 1

2

1

2

−ls

H x

Fig. A11. Sense of the sign of the inclination angle.

(nose point) 1. Numbers 1 and 2 designate the ends of the cutting edge. As such, if the tool tip 1 is located below point 2, the inclination angle λs is positive; if points 1 and 2 are at the same level, λs = 0; and when the tool tip 1 is located above point 2, then the inclination angle λs is negative. The sign of the inclination angle defines the chip-flow direction, as shown in Fig. A12. When λs is positive, the chip flows to the right and when λs is negative, the chip flows to the left. The direction of chip flow, however, is defined not only by λs , but also by the cutting edge angle κr . These two angles define the spatial location of the tool cutting edge. In turn, the spatial location of the cutting edge constrains the location of these planes, since the cutting edge is the line of intersection of the rake and flank planes. The complete location of the rake plane is then defined when the normal rake angle γn is known and the location of the flank planes is fully defined when the normal flank angle αn is known. Simple relationships exist among the angles considered in the tool-in-hand system. These relationships have been derived assuming that the tool-side rake angle γf , the tool-back rake angle γp and the tool cutting edge angle κr are the basic angles for the tool face, and the tool side clearance angle αf , the tool back clearance angle αp , and the tool cutting edge angle κr are the basic angles for the tool flank tan λs = sin κr tan γp − cos κr tan γf

(A20)

tan γn = cos λs tan γo

(A21)

tan γo = cos κr tan γp + sin κr tan γf

(A22)

cos αn = cos λs cot αo

(A23)

cot αo = cos κr cot αp + sin κr cot αf

(A24)

410

Tribology of Metal Cutting

+ls f

−ls f

Fig. A12. Influence of sign of the inclination angle on the direction of chip flow.

It must be stated, however, that some of these relationships apply only when the cutting edge angle κr is less than 90◦ . Nowadays, it is a common practice to use cutting tools having κr greater than 90◦ . Moreover, most of the drills are made in the same way. For these tools, the following relationships are valid tan λs = − sin κr tan γp − cos κr tan γf

(A25)

tan γo = cos λs tan γo

(A26)

tan γo = − cos κr tan γp + sin κr tan γf

(A27)

cot αn = cos λs cot αo

(A28)

cot αo = − cos κr cot αp + sin κr cot αf

(A29)

A4 Determination of Uncut Chip Thickness for a General Case Section A3 defines the uncut chip thickness for the simplest case where a single-point cutting tool is used for turning (Fig. A7). Because the uncut chip thickness defines to a large extent the tribological conditions of any cutting operation, its proper determination for the whole variety of the cutting tools should be provided. Unfortunately, none of the books contains such a material, and so tool designers, manufacturing specialists and practitioners in the field have no reference to turn to in the determination of uncut chip thickness for many cutting operations besides turning, milling and drilling. As a result, the determination of the true uncut chip thickness is not carried out in the design and analysis of many tools. Further considerations are based on the method proposed by Rodin [6] and further developed by Astakhov et al. [7,8].

Basics, Definitions and Cutting Tool Geometry

411

The uncut chip thickness for any machining operation at a given point of the cutting edge is determined as t1 = f cos χf ,

(A30)

where χf is the angle between the feed direction and the normal to the tool cutting edge plane at the point of the cutting edge considered. This angle can be considered as the tool cutting edge angle in the tool-in-use system. Generally, angle χf is considered in the 3D plane containing the vectors of the feed motion and the normal to the tool cutting edge plane at the point considered. Note that this plane is always the main reference plane in the tool-in-use system of consideration of the tool geometry. The direction of feed for a tool working with several feed motions is determined by the vector summation of the directions of all these feeds. This should not present any problem as these directions are well known. As angle χf is between the feed direction f and the normal N to the tool cutting edge plane at the point of the cutting edge considered, the angle between these two vectors is determined as cos χf =

f ×N f N

(A31)

and thus the uncut chip thickness is then calculated as t1 =

w

x df

f ×N N

(A32)

vf

z Ri

f

A A

a kr

B

y

y

Fig. A13. Determining the uncut chip thickness in thread cutting.

412

Tribology of Metal Cutting

Consider the determination of the uncut chip thickness t1 in a thread-cutting operation as an example of the use of the proposed methodology. A model of this operation is shown in Fig. A13. A thread cutting is fed incrementally after each pass by feed f in the direction of f so the cutting edge AB does the entire cutting. In this model, vector a is a unit vector along the cutting edge so it always lies in the tool cutting edge plane in any system of consideration. The xyz coordinate system is set, as shown in Fig. A13. In this coordinate system, the vector of the cutting feed f is determined by its projection on the corresponding coordinate axes as f = if cos δf − jf sin δf

(A33)

a = i cos κr + j sin κr

(A34)

and unit vector a as

If Ri is the location radius of point A of the cutting edge, the velocity of this point in its spiral motion is vA = iνf + ω × Ri = iνf + kωRi ,

(A35)

where νf is the velocity of the tool in the x direction. It is understood that νf = knp,

(A36)

where k is the number of starts of the thread being cut, n is the number of revolutions per second of the vortices (rpm/60) and p is the thread pitch. A normal S to the tool cutting edge plane in the tool-in-use system is determined by the cross product of vectors vA and a located in this plane as ' ' i ' N = a × vA = '' cos κr ' νf

j sin κr 0

k 0 ωRi

' ' ' ' = iωRi sin κr + jωRi cos κr − kνf sin κr ' ' (A37)

and its modulus  N = ω R2i + h2h sin2 κr ,

(A38)

where hh = νf /ω is the helix parameter. Using Eq. (A32), one can obtain   f Ri sin κr + δf ωRi sin κr cos δf + ωRi f cos κr sin δf t1 = =   ω R2i + h2h sin2 κr R2i + h2h sin2 κr

(A39)

Basics, Definitions and Cutting Tool Geometry

413

As shown, the uncut chip thickness varies along the cutting edge because radius Ri differs for each of its point. In a particular case of bar turning, δf = 0 and hh = 0, thus Eq. (A39) becomes t1 = f sin κr

(A40)

which is the same as Eq. (A3) obtained earlier for this case.

References [1] Astakhov, V.P., Metal Cutting Mechanics, CRC Press, Boca Raton, USA, 1998. [2] Oxley, P.L.B., Mechanics of Machining: An Analytical Approach to Assessing Machinability, John Wiley & Sons, New York, USA, 1989. [3] Klushin, M.I., Metal Cutting: Basics of Plastic Deformation of the Layer Been Removed, Mashgiz, Moscow, Russia, 1958. [4] Stabler, G.V., The chip flow law and its consequences. In Proceedings of the 5th International MTDR Conference, 1964. [5] Colwell, L.V., Predicting the angle of chip flow for single point cutting tools, Transactions of the ASME, 76 (1954), 199–202. [6] Rodin, P.R., The Basics of Shape Formation by Cutting (in Russian), Visha Skola, Kyev, Ukraine, 1972. [7] Astakhov, V.P., Galitsky, V.V., Osman, M.O.M., A novel approach to the design of self piloting drills. Part 1. Geometry of the cutting tip and grinding process, ASME Journal of Engineering for Industry, 117 (1995), 453–463. [8] Astakhov, V.P., Galitsky, V.V., Osman, M.O.M., A novel approach to the design of self-piloting drills with external chip removal. Part 2: Bottom clearance topology and experimental results, ASME Journal of Engineering for Industry, 117 (1995), 464–474.

APPENDIX B

Experimental Determination of the Chip Compression Ratio (CCR)

B1 General Experimental Techniques Although a number of experimental methods for the determination of the chip compression ratio (CCR) were known to researchers, modern books and other publications on metal cutting do not consider any of them because CCR is not regarded as an important parameter in metal cutting studies. Because it is argued in this book that major tribological parameters and characteristics of metal cutting correlate with CCR, a need to present a few common experimental methods for the determination of CCR is felt. The simplest method is to measure the chip thickness and then calculate CCR as ζ = t2 /t1 ,

(B1)

where t2 is the chip thickness and t1 is the uncut chip thickness. However this is not always possible because the chip: (a) might have a saw-toothed free surface and (b) be very small and 3D-curved. The second method is the weighing method. A small (5–10 mm long) straight piece of the chip is separated from the rest of the chip. Then, its length Lc and width dw1 are measured. When the piece of the chip selected for the study is not straight, a computer vision system available nowadays in most shops is used to measure its length properly. Then, it is weighed so its weight Gch (N) is determined. The chip thickness is then calculated as t2 =

Gch , dw1 Lc ρw g

(B2)

where ρw is the density of the work material (kg/m3 ) and g = 9.81 m/s2 is the gravity constant. 414

Experimental Determination of the Chip Compression Ratio (CCR)

415

For finishing operations when the depth of cut is shallow, it becomes rather difficult to measure the width of the chip. CCR is determined in this case using the ratio of the chip and the uncut chip cross-sectional areas, Ach and Aw , respectively, i.e. ζ=

Ach Aw

(B3)

As such, the cross-sectional area of the chip is determined using the weighing method as Ach =

Gch Lc ρ w g

(B4)

and the cross-sectional area of the uncut chip is determined as Aw = dw f,

(B5)

where dw is the depth of cut and f is the cutting feed. The third method is the direct method, which is applicable in turning, milling, drilling and other common machining operations. The essence of this method is that the workpiece is “marked” before cutting and then the resultant marks on the chip are compared with the original marks. The realization of this method for longitudinal turning is shown in Fig. B1(a). As shown, two longitudinal grooves are made on the outer surface of the

hw

A

View A Lg1

(a) TURNING dw

Lg 2

Workpiece Workpiece

Fragment of the chip

f Tool

(c) MILLING

(b) DRILLING Ll

SECTION A-A

A

A

Ll

h1

Ød1 h

Lc

Ød ØD

Fragment of the chip

Workpiece

Lc

Workpiece Axis of the tool

Trajectory of cutters

Fig. B1. Practical methods of determining CCR.

Fragment of the chip

416

Tribology of Metal Cutting

workpiece before testing and the arc distance between these grooves Lg1 is measured. After the test, a chip section with these marks can be easily found and the distance Lg2 is measured. CCR is then determined as ζ = Lg1 /Lg2

(B6)

The realization of the method discussed to measure CCR in drilling is shown in Fig. B1(b). Two small holes of diameter d1 are drilled as shown in Fig. B1(b) along the trajectory of the point of the drill cutting edge. Diameter d2 is smaller than that (D) of the would-be-hole. The arc distance Lg1 between the centers of these holes is measured. After the test, a chip fragment having marks from the two holes is found and the arc distance Lg2 between their centers is measured at high magnification using an optical comparator or a computer vision system. Using Eq. (B6), CCR is determined. The realization of the discussed method for face milling is shown in Fig. B1(c). As shown, the surface of the workpiece is made with a step having width Lg1 = 3–6 mm and height which is 4–6 times smaller that the depth of the cut, i.e. dw /hw = 4–6. After the test, the width Lg2 is measured and CCR is determined using Eq. (B6). Shifting the position of the axes of the tool and the workpiece, one can determine CCR under a wide range of uncut chip thickness.

B2 Design of Experiment Approximation of the dependence of CCR on the factor “vt1 ” (the Peclet criterion) can be accomplished using a simple test program consisting of only two runs. For example, for the test results of which shown in Fig. 2.8, the following simple design of experiment can be utilized. Table B1 shows the plan of tests. Using these test results, CCR can be approximated as follows:  ζ = ζ0 √

vt 1 (vt 1 )2 /(vt 1 )1

xζ (B7)

,

where ζ0 =

 √ ζ1 ζ2 = 2.60 × 1.93 = 2.24

Table B1. Plan and test results. Test number (i) 1 2

103 vt1 (m2 /s)

CCR (ζi )

0.25 1.85

2.60 1.93

(B8)

Experimental Determination of the Chip Compression Ratio (CCR)

417

and xζ =

ln (ζ2 /ζ1 ) ln (1.93/2.60) = −0.15 = ln [(vt 1 )2 /(vt 1 )1 ] ln [1.85/0.25]

(B9)

Finally 

vt 1 ζ = 2.24 0.68 × 10−3

−0.15



0.25 × 10−3 < vt 1 < 2 × 10−3



(B10)

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419

Index 2k Factorial experiment, 294 Amplitude, 105, 107 ANSI/ASME Tool Life Testing, 221, 276 Apparent coefficient of friction, 127, 173, 184 Asperities, 126 ASTM Manual on the Use of Thermocouples in Temperature, 204 ASTM Standard tests, 334 Asymmetric deformation, 141 Bending moment, 15, 84 Body contact, undeformed/loaded, 137 Boussinesq solution, 140 Briks criterion, 187, 193 Brinell hardness, 178 Built-up edge, 83 Card model, 3, 8 Catastrophic tool failure, 211 Charge-coupled device (CCD) camera, 200, 278 Charpy values (CVN), 231 Chemical adsorption (chemisorption), 358 Chip compression ratio (CCR), 11, 76, 80, 89–91, 150, 153–154, 167–169, 174, 185. See also Poletica criterion; Plastic deformation correlations with the forces on the flank, 184–185 experimental determination, 414–416 influence of adhesion properties of the work and tool materials, 169 influence of surrounding media, 174 influence of the cutting speed, 171–173 influence of the thermoconductivity of the work material, 176 influence of the tool–chip contact temperature, 167 Chip deformation, energy loss, 96

Chip formation, 1–63, 111, 155, 286 frequency, 53 work materials brittle, 25 ductile, 29 highly ductile, 33 Chip formation models, applicability, 60 computer numerical control (CNC), 60 Chip forming zone, 71–73, 97 Chip temperature, 86 Chip thickness, 103 Chip velocity, 97 Coatings, 372 selection notes, 376 Coating application techniques chemical vapor deposition (CVD), 373–374 dynamic compound deposition (DCD), 374 physical vapor deposition (PVD), 373–374 thermal diffusion (TD), 374–375 Coating–substrate interface, 374 Cochran’s criterion, 301 Coefficient of friction, 127 Coherent energy waves, 100 Component methods of improving tribological conditions, 326 Computer aided manufacturing (CAM), 368 Confidence interval, 302 Contact length, 149–151, 157, 175, 187, 195. See also Uncut chip thickness Coolant, see Cutting fluid Cooling action, 338–339 air-cutting fluid mixture (mist), 348–351 cooling intensity, 341–342 direct, 340 due to evaporation, 343–348 embedded heat pipe in the tool, 351–355 embrittlement, 355 energy balance, 338–339 Correlation diagram, 288–289, 291 Correlation table, 289, 292 Coulomb friction, 125

420 Critical internal energy, 85 Cross-validation criterion, 319 Cut-in period, 147 Cutting edge, 23, 179 active length, 195 angle, 103 radius, 97, 197, 407–408 Cutting feed, 109, 239–240, 242–243 Cutting fluids (coolants) application, 331–332 corrosion resistance, 368–369 cost, 370 cryogenic fluid, 367 emulsions, 365 foam tendency, 369 penetration into contact interfaces, 336–338 practical considerations in the final selection, 368 safety/health, 369–370 selection, 330 selection, 330–334, 368–372 semi-synthetic fluids, 366 stability, 370 straight oils, 364–365 synthetic fluids, 365 waste treatability, 368 Cutting fluid, trying and testing, 331 actual cutting under controlled conditions, 354–355 rubbing test, 332–334 trying out on a machine, 331 Cutting inserts, 106 Cutting operations, 83 Cutting parameters, 239 Cutting power/force, 16, 338 Cutting process, 109 Cutting regime, 107, 117 Cutting speed, 82, 84, 111, 130–133, 135, 158, 162, 170–173, 197–198, 338. See also Chip compression ratio influence of, 43, 104, 237 Cutting system efficiency, 91–92 energy balance, 94 energy partition, 69 physical efficiency, 73 Cutting theory, xii, 4, 20, 78, 91, 190, 210, 243, 336 Cutting temperature, 197–198, 227 influence of the cutting speed, 235, 237 Cutting tool, 69, 71 chip formation cycle, 154

Index geometry, 114, 117 physical resource, 220 tool wear, 220 trajectory, 102 Cutting wedge, 23, 72, 259–266, 269 angle, 194, 396–397 breakage, 264, 266 creep, 259 plastic lowering, 265–266 resource, 269 Deformation/thermal longitudinal waves, interaction of, 108, 113 Deformation velocity, 87, 111 Deformation wave, wavelength of, 110 Deformation zone, 124 Depth of cut, 110, 239, 244–245 Design matrix, 286–288, 294–297, 306, 310–315, 417 orthogonality, 297 properties, 295–297 Design of experiments (DOE), 277, 417 basic terminology, 277 errors, 279 pre-process decisions, 283 requirements to test conditions, 279 screening DOE, 281 sieve DOE, 282 Diamond-like coating (DLC), 378 Difficult-to-machine material, 91, 254, 269 Dimension tool life, 224–227, 244, 253 Dimension wear rate, 225 Distribution law of normal pressure, 145 Dry machining, 329–330 Ductility, 231, 233 Dundrus’ constant, 138 Dynamic phenomena, 312–318 Dynamometer, 75, 182 Easy-to-machine material, 91 Elasticity modulus, 84–85 Electromotive force (e.m.f.), 250 Electronic voltmeters, 205 Elongation at fracture, 120 Energy consumption, 117 Energy exchange, 69 Energy flows, 70 chip energy, 71 chip formation zone, 71, 82, 84 cutting tool energy, 71 Energy loss, 95 Energy of failure, 101

Index Energy waves, experimental verification, 103 interaction, 99 internal energy, 99 wavelengths, 112 Errors/inaccuracies, 280–281 Extreme pressure (EP) additives, 337 Extreme pressure properties, 332 Factor, 278 code value, 295 compatibility, 284 controllability, 283 effect, 290 independence, 284 interval of variation, 295, 303 levels, 298, 306 significance, 290, 293 zero level, 295, 302–303 Falex Pin and Vee Method, 332 Falex Tapping Torque Test Machine, 334–335 FEM analysis, 146–147 model, 126, 145 Film condensation, 353 F-criterion of Fisher, 304 First cutting law (Makarow’s law), 229 consequences, 234 Flank, 97 Flank angle influence, definition, 405–406 Flank contact surface, 179 Flank forces, 177, 183 Flow-shear stress, 91 Force acting along the shear plane, 9, 15 cutting, 13, 15–16 friction, 13 normal, 13 thrust, 13 Fractional factorial experiment, 282 Fracture strain, 117–118 Free cutting, 394 Friction angle, 3, 7 Frequency of chip formation, 53 influence of the cutting speed and work material, 57 Gradient, 278 Group Method of Data Handling (GMDH), 307–323 algorithm, 320–322

421 Artificial intelligence (AI), 307 Neural network (NN), 307 Gundrilling, 284, 302 components, 284 cutting conditions, 287 cutting fluid/coolant, 287 design/geometry, 284–286 design matrix, 286, 288, 305–306 machine, 286 tool life criteria, 287, 294 work material, 287 Half-plane indentation, 139 Heat conduction, Fourier law of, 353 Heat transfer coefficient, 349–350, 352 High-speed machining, 113 Homogeneity, variance, 301 Hooke’s law, 79 Hydrostatic stress, 117–118 Inclination angle, 408–409 Internal energy principle, 99 Interactions of energy waves, 99 influence on the cutting force, 102–114 Japan, Society for Precision Engineering (JSPE), 22 Kolmogorov criterion, 312 Kolmogorov–Gabor polynomial, 309 Loading-unloading system, 69 Lode stress parameter, 116–118 Log–log plot, 81 Low/high temperature creep, 256–258, 260–261 Low-energy chemical reactions, 360 Lubricity tests, 334 Machinability, 88, 379–386 Machining zone, 99 Makarow’s law, 227, 229–230, 234 Mathematical model DOE, 278–279, 282–283, 297, 300, 302, 305, 318–320, 322 adequacy, 303 for the roundness of the gundrilled hole, 304 of tool life, 306 Mean contact temperature, 167 Mean normal contact stress, 161–162, 164, 171, 176. See also Poletica criterion Machining at optimum cutting temperature, 229

422 Mean shear stress, 158, 160–161, 175 Mean stress variation, 120 Medium temperature CVD (MTCVD), 374 Metal cutting, 23 temperature assessment, 191 tests, 276 thermal analysis, 211 Microstructural methods, 199 Minimum quantity lubricant (MQL), 330, 348–351 Model of chip formation, 21. See also single-shear plane model for brittle work materials, 26 for cutting with a high rake angle, 40 for ductile work materials, 30 for saw-toothed chip formation, 48 generalized, chip shape classification, 23 influence of the cutting speed, 43 when seizure occurs, 37–39 Modulus of elasticity, 95 Molecular diffusion, 88 Multi-layer coating, 377 Mutual adhesion properties, tool/work materials, 167, 173, 176 Natural contact length, 156 Near-dry machining, see Minimum quantity lubricant Non-free cutting, 394 Number of degrees of freedom, 291, 303 Nusselt number (Nu), 340 Oblique cutting, 394 basic terms, 383 Optimal cutting speed, 230–231, 234 Optimal cutting temperature, 227, 229, 231, 234–238, 242–246, 250, 254 experimental determination, 231 cutting operations, 230 influence on the properties and metallurgy of the work material, 232–234 methods of determination, 237–239 Optimal tool life, 244 Organic SAAs chlorine-substituted, 358 iodine-substituted, 358 Orthogonal coordinate system, 104 Orthogonal cutting, 114, 136, 392 Pareto analysis, 293 Péclet number (number), 87–88, 99, 193 Peierls–Nabarro stress, 233

Index Physical adsorption, 360 Physical efficiency of the cutting system, 74 concept and determination through cutting force, 74–75 determination through the chip compression ratio, 75 influence of the cutting feed, 93 influence of the depth of cut, 93 influence of the rake angle, 92 methods of improving, 98 Physical vapour deposition (PVD), 199 coatings, 374–375 Physisorption, 357 Plackett–Burman design, 282 Plastic deformation, 73, 76–97, 256, 261. See also Shear strain chip compression ratio (CCR), 76–77, 80, 86, 91 chip deformation, 77 equilibrium, 78 force/stress equilibrium, 78 geometrical deformation, 77 measures, 76 metal-deforming process, 76 shear-flow stress, 76 Plastic lowering, 254–269 cutting wedge structure, 284 fractography of breakage due to lowering, 264 influence of the cutting feed and speed, 256–257 intensification due to seizure, 259 model, 260, 265 reduction, 266 Plastic strain parameter, 116 Poisson’s ratio, 79, 95, 117, 137 Poletica criterion (Po-criterion), 152–155, 164, 175 influence of CCR, 153–156 Polycrystalline diamond (PCD), 326, 378 Prandtl number (Pr), 341 Pre-process decisions, 279, 283 compatibility, 284 controllability, 283 independence, 284 Principal stress, 115 Radial tool wear, 249 Rake angle, 91–92, 97, 148, 152, 161, 165. See also Contact length definition, influence, 403–405 Rebinder effect, 355–357

Index Regression coefficient, 299 Regression model, 294 Regularity criterion, 319 Relative sharpness similarity criterion, 193 Relative tangential displacement, 138 Resource of the cutting wedge, 269 correlation between total work and flank wear, 270 correlation curves, 273 critical work, 269 Resonant frequency, 103 Response, 277 Reynolds number (Re), 340 Saw-toothed chip, 48–53 FEM, modeling, 50–51 instrumented hardness tests, 52 system formation, 49 Scatter diagram, 292 Screening test, 281–282 segmental saw-toothed chip, formation, 55–57 Semi-dry machining, see Minimum quantity lubricant Shear angle, 3–8, 15 Shear-flow stress, 113 Shear plane, 3–8 Shear strain, final, 6–7, 10–11, 80 Shear (frictional) stress, 126 Shear stress, definition, 140 Shear/stress distributions, 134 Sieve test, 293 Similarity criterion, 187, 194–195 Sine wave, wavelength of, 109 Single-point turning tools, 221, 276 rake face/crater wear, 221 relief face/flank wear, 221 Single-shear plane model, 1–20 Brik’s model, 4 Card model, 8 deformation zones, 5 drawbacks, list, 20 Merchant solution (theory), 18 plastic deformation, 5 scanning electron microscope (SEM), 11, 46–47 shear stress/normal stress, 19 specific shear angle, 6 specific shear plane, 6 Time model, 3 tool-chip interface, 5 velocity diagram, 9–10, 12 Zorev’s model, 6

423 Sinusoidal periodic data, 104 Sliding, 124, 144 velocity, 124 Solid film lubricants, 332 Solid-state solutions, 168 Specific dimension tool life, 227–228 Specific heat, 88 State of stress, 114 calculation from the tensile test data, 119–120 influence of the strain at fracture, 115–118 Statistical criteria of Fisher (F-criterion), 301, 303–304 Standard deviation, 290 Steady-state thermodynamic analysis, 87 Steady-state wear, 223 Sticking friction, 126 Strain-hardening coefficient, 81 Strain rate, 9, 83 Stress triaxiality, 114–115 Stress/elongation at fracture, 119 Stress-strain curve, 75, 81 true stress–strain curve (flow curve), 81 Stress–strain relationship (Prandtl), 116 Structure of manufacturing costs, 329 Student’s t-criterion, 290, 301 Super hard tool materials, 339 Superimposed hydrostatic pressure, 119 Surface-active agents (SAA), 358 Surface wear rate, 227–228, 240 System model, interface stress distributions, 145 System rigidity, 248 Systemic methods of improving tribological conditions, 327 Taylor’s tool life formula, 224 Temperature at the contact interfaces, 189 analytical/numerical methods, 191 similarity methods, 192–199 microstructural methods, 199–200 Temperature Measurement calibration procedure, 209 embedded thermocouple, 204–205 infrared thermography, 200, 202 natural thermocouple, 209 running thermocouple, 206 thermocouples, 204 tool–work thermocouple, 207–208, 210–211 Temperature–deformation stress relaxation, 260 Temperature–hardness curves, 237, 239

424 Temperature–speed (cutting) factor, 150 Thermal conductivity, 72, 88, 96 Thermal diffusivity, 88, 102 Thermal energy, 72, 98, 338 Time–temperature transformation (TTT) diagrams, 199 Tool–chip contact area, 241 length, 125, 168, 169 elastic zone, 87, 134 influence of adhesion properties of the work and tool materials, 169 influence of the cutting speed, 151 influence of the rake angle, 152 influence of the uncut chip thickness, 150 influence of the work material, 151 influence on the normal stress, 157 plastic zone, 134–135 Tool–chip interface, 71, 78, 84, 125, 135, 140, 220, 224, 227, 231, 241, 244, 247, 256, 258–259, 269, 273, 327 basic tribological characteristics, 125 characteristic points, 141 contact normal stress influence of the cutting speed, 162, 170 influence of the Poletica criterion, 164 influence of the rake angle, 163 contact shear stress correlation with CCR, 161 correlation with the ultimate tensile strength, 160 influence of the contact temperature, 159 influence of the cutting speed and rake angle, 158, 170 contact stress distributions, 128 contact stress measurement experimental sliplinefield method, 130–134 photoelastic method, 128–130 split tool method, 130–132 friction coefficient, 125 modeling FEM, 145–149 modeling, analytical 134–145 Tool cutting edge angle definition, 397–398 significance, 399–403 Tool failure, 254 Tool geometry, 107, 323, 391–412 angle of cut, 247 angles, definitions, 396 chip thickness, 240, 245, 249 chip width, 245

Index flank angle, 247, 259 parameters, 245 rake angle, 3, 6–8, 11, 247, 249, 267 rake surface, 245, 266 reference plains, 394–396 tool nose radius, 245, 259, 266 tool-in-hand system, 396–397 Tool life, 167, 220, 222, 304 dimensional tool life, assessment criteria, 225 inconsistency, 113 influence of cutting feed under optimal cutting temperature, 243 influence of the cutting feed and depth of cut, 239 influence of the tool geometry, 245 influence of the workpiece diameter, 248 specific dimensional tool life, 226 Taylor’s tool life formula, 224 testing, 237, 310–322 Tool material, influence 165–166, 168 Tool rake face, 156, 164–165 Tool wear curves, 222 dimensional wear rate, 225 influence of the cutting speed, 235, 246 surface wear rate, 226 types, 221 volumetric (mass) tool wear, 225 wear patterns, 226 Tool–workpiece interface, 177 modeling, similarity methods, 18 normal and shear stress distributions, 181 Zorev’s results, 177 Tool wear rate, 240–242, 245, 247, 250 assessment, 224 Transition temperature range, 233 Tresca, 3 Tribological characteristics, assessment, 179–191 Tribological condition improvement component method, 326–327 property modification (work material), 368 systemic method, 327 Tribological interfaces, 87 Tribology, 94 Uncut chip thickness, 149–150, 197 definition, 399–403

Index determination, 410–412 influence on the axial force, 316 influence on the drilling torque, 317 Uniaxial tension, 115 van der Waals-type forces, 357 Variance homogeneity, 301 Variance, raw, 300 Variance of adequacy, 303 Variance of response, 300 Vector of input variables, 311 Velocity diagrams, 10–11 normal to the shear plane, 11 of chip, 9 of shear, 9, 12 Volterra functional series, 308 Volumetric/mass tool wear, 225, 228 von Mises yield criterion, 116 von Mises’ stress, 79 Water-based cutting fluid, 346 Wave-interaction force component, 109 Wavelength, 105, 107

425 Work material, 165, 168, 171, 174, 183, 194, 379 machinability grain size, 383 heat treatment, 381 minor elements, 385 Work of plastic deformation in metal cutting, 76 elementary, 81 total, 81 influence of the cutting speed, 82–87 Workpiece, 69 diameter, 103, 110, 248–254 rotational speed, 111 Worn volume, 226 X-ray microanalyzer, 337 Yield shear strength, 187 Young’s modulus, 231 Zorev’s analysis/results, 177–179 Zvorykin, 3

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(a) T e m p e ra tu re (C ) 500 466 432 398 364 330 296 262 229 195 161 127 93 59 25

(b) T em p e ra tu re (C ) 500 466 432 398 364 330 296 262 229 195 161 127 93 59 25

(c) Stress-XX (MPa) 3.00E+02 1.71E+02 4.29E+01 -8.57E+01 -2.14E+02 -3.43E+02 -4.71E+02 -6.00E+02 -7.29E+02 -8.57E+02 -9.86E+02 -1.11E+03 -1.24E+03 -1.37E+03 -1.50E+03

(d) Stress-XX (MPa) 3.00E+02 1.71E+02 4.29E+01 -8.57E+01 -2.14E+02 -3.43E+02 -4.71E+02 -6.00E+02 -7.29E+02 -8.57E+02 -9.86E+02 -1.11E+03 -1.24E+03 -1.37E+03 -1.50E+03

(e)

(f)

Fig. 1.33. FEM modeling of the formation of saw-toothed continuous fragmentary chip: (a) and (b) shape of the chip, (c) and (d) temperature distribution, (e) and (f) stress distribution (Courtesy Prof. J.C. Oureiro).

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