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Mechanics of machining with chamfered tools Ren, Haikun 1998

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M E C H A N I C S  O F M A C H I N I N G W I T H  C H A M F E R E D  By Haikun Ren B. Sc. Chengdu Technological University, RR. China  A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF T H E REQUIREMENTS FOR T H E D E G R E E OF M A S T E R O F A P P L I E D SCIENCE  in T H E F A C U L T Y O F G R A D U A T E STUDIES D E P A R T M E N T O F MECHANICAL ENGINEERING  We accept this thesis as conforming to the required standard  T H E UNIVERSITY OF BRITISH COLUMBIA  March 1998 © Haikun Ren, 1998  TOOLS  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis forfinancialgain shall not be allowed without my written permission.  Department of Mechanical Engineering The University of British Columbia 2324 Main Mall Vancouver, Canada V6T 1Z4  Date:  Abstract  High speed machining of hardened steels is the recent preferred manufacturing technology in die and mold manufacturing technology. P20 tool steel is the most widely used material in injection molding dies, and its high speed-high productivity machining is the focus of this thesis. P20 has an average hardness of 35 Rc. High speed cutting of P20 is constrained by chatter vibrations, accelerated tool wear and chipping of cutting tool edges. The chamfered cutting tools are used in machining hardened steels due to their increased strength of cutting edges. An analytical model, which allows the evaluation of cutting forces, stress and temperature distribution for cutting tools with chamfered edges, is studied in this thesis. The cutting process is modeled at three distinct zones by extending the slip line field proposed by Oxley et al. [36]. The primary and secondary deformation zones are treated similar to the work of Oxley, but the flow stress characteristics of the work material are calibrated from orthogonal cutting tests, as opposed to high-speed compression or tensile tests. The chamfer zone is modeled by assuming dead metal trapped over the chamfered edge. The trapped metal is assumed to be stationary and the metal flows around it similar to the extrusion process. The contact between the rake face and chip is assumed to have equal sticking and sliding lengths, and the total contact length is measured experimentally. Theflowstress of the material in all three zones are expressed as a function of temperature, strain and strain rate. The deformation and friction energy in all three zones are evaluated individually, and summed to find the total energy consumed in forming the chip. By applying the minimum energy principle to total energy consumed, an average shear angle in the primary shear deformation zone is predicted. The overall analytical model allows evaluation of stress, temperature and cutting forces contributed in each deformation zone for a given set of cutting conditions and  u  chamfered cutting tool geometry.  The predicated and experimental results obtained from  orthogonal turning of P20 steel with ISO S10 carbide and Cubic Boron Nitride (CBN) tools agreed well. The model and experimental results indicate that the optimal chamfer angle is about -15 degrees, and optimal cutting speeds are about 240 m/min and 500 m/min for ISO S10 carbide and CBN tools, respectively. The model predicts a rake face temperature, which is just under the diffusion limit of binding materials for S10 and CBN tools at the optimal cutting speeds and chamfer angle.  iii  Table of Contents  Abstract  ii  List of Tables  v  List of Figures  vi  Acknowledgement  vii  Nomenclature  viii  1  Introduction  1  2  Literature Review  4  2.1  Introduction  4  2.2  Mechanics of Orthogonal Machining with Sharp Edge Tools  6  2.2.1  Classical Shear Plane Models  6  2.2.2  Oxley's Shear Zone Model  2.3  3  10  Mechanics of Orthogonal Cutting with Chamfered Edge Tools  16  2.3.1  The Effect of Tool Edge Geometry on the Cutting Process  16  2.3.2  Zhang's Three Zone Model  19  2.3.3  Summary  19  Modeling of Machining with Sharp Tools  20  3.1  Introduction  20  3.2  Modeling of Plastic Deformation in Cutting with Sharp Tools  20  iv  3.3  3.2.1  Stress and Strain  20  3.2.2  Plastic Deformation in the Primary Shear Zone  27  3.2.3  Plastic Deformation in the Tool-Chip Interface Zone  29  Experimental Modeling  32  3.3.1  Experimental Setup  33  3.3.2  Experimental Procedures  36  3.3.3  Modeling of Flow Stresses and Strain Hardening Under High Strain Rate and Temperature Through Machining Tests  3.4  3.5 4  Prediction of Cutting Process with Sharp Tools  56  3.4.1  A Minimum Energy Approach  56  3.4.2  Model Verification  61  Summary  80  M o d e l i n g of Machining with Chamfered Tools  84  4.1  Introduction  84  4.2  Modeling of Plastic Deformation for Cutting with Chamfered Tools  86  4.2.1  Plastic Deformation in the Primary Shear Zone  88  4.2.2  Plastic Deformation in the Chamfered Edge Zone  89  4.2.3  Plastic Deformation in the Tool-Chip Interface Zone  93  4.2.4  Prediction of Cutting Process with Chamfered Tool  95  4.3  5  47  Model Verification  100  4.3.1  Chamfer Tools Used in Machining Tests  101  4.3.2  Predicted and Experimental Results  102  4.3.3  Summary  116  Conclusions  118  v  Bibliography  123  Appendices  129  A Temperature in the Primary Shear and the Tool-Chip Interface Zones 129 B Mapping Flow Stresses in the machining process  131  C Identification of Edge Forces  133  vi  L i s t of Tables  3.1  Chemical composition of P20 mold steel  33  3.2  Mechanical properties of P20 Mold steel  35  3.3  Cutting conditions  41  3.4  Machining test data (" sharp tool "), w=3.6 mm  44  3.5  Machining test data (" sharp tool "), w=5.0 mm  47  3.6  Flow stress <T\, strain hardening index n, cutting temperature TAB obtained from machining test data  51  3.7  Flow stress o-i , cutting temperature T ;  4.1  Cutting conditions and chamfer geometry for the prepared chamfered edge tools  nter  nter  obtained from machining test data  53  used in machining tests, width of cut w=3.6 mm, main rake angle a = 0°. D  P20 work material: hardness 34 HRC, Composition: C 0.37%, S 0.3%, M t  n  1.4%, C 2.0%, N{ 1.0%, M 0.2%. SANDIVIKS10 carbide tool: WC 36.1%, r  0  TiC 39.3%, T C 8.6%, C 11.0% a  4.2  101  0  Cutting conditions and chamfer geometry for the CBN (MITSUBISHI MB820) chamfered edge tools used in machining tests. Average width of cut w=2.55 mm, main rake angle a = —5°. CBN tool material composition: CBN 50%, 0  (TiN and Al O ) 50% 2  102  s  vii  List of Figures  2.1  Diagram of orthogonal cutting  5  2.2  Force diagram in Merchant's model  7  2.3  Chip formation model proposed by Lee and Shaffer [22]  9  2.4  Force diagram of orthogonal cutting proposed by Albrecht [32]  10  2.5  Chip formation model proposed by Oxley and his coworkers  12  2.6  Heat Sources in Cutting Process  15  2.7  Mechanism of SWC cutting  17  2.8  Cross-section of the end of planer chip cutting with SWC tool [15]  18  3.1  State of stresses in plane plastic flow  21  3.2  Velocity diagram in chip formation  26  3.3  Distribution of normal and shear stresses at the tool-chip interface  30  3.4  Diagram of experimental setup for orthogonal machining of P20 mold steel . . 34  3.5  Shaft used in machining tests  37  3.6  Hardinge CNC turning center used in machining tests  38  3.7  Workpiece used in machining tests  39  3.8  SANDVIK carbide insert  40  3.9  Illustration of measurement of contact length l and tool wear land VB from c  the cutting tool  42  3.10 Plot of correlation of contact length with cutting speed V and undeformed chip w  thickness t-i, w=3.6 mm  45  viii  3.11 Plot of correlation of shear stress on the shear plane with cutting speed V and w  undeformed chip thickness t\, w=3.6 mm  46  3.12 An algorithm of the cutting temperature estimation  50  3.13 Flow stress, strain hardening index, shear strain, shear strain rate, and cutting temperature versus different cutting conditions  55  3.14 A generalized cutting process evaluation algorithm for cutting with sharp edge tools  57  3.15 Predicted shear angles by Merchant's [21]and Lee and Shaffer's [22] shear angle solutions  62  3.16 Comparison of predicted shear angles by the proposed model with experimentally evaluated shear angles, w=3.6 mm, a = 0°, V : 240, 380, 600 m/min. . . 64 a  w  3.17 Comparison of predicted shear angles by the proposed model with experimentally evaluated shear angles, w=3.6 mm, a = 0°, W. 0.06, 0.08, 0.10 mm. . . . a  65  3.18 Variation of experimentally measured contact length l and friction angle 8 c  with cutting speed V  66  w  3.19 Predicted and experimentally determined friction angles versus various cutting speeds, w=3.6 mm, a = 0°, h: 0.06, 0.08, 0.10 mm a  68  3.20 Predicted and experimentally determined friction angles versus various undeformed chip thickness, w=3.6 mm, a = 0°, V : 240, 380, 600 m/min Q  w  70  3.21 Predicted and experimentally determined cutting energy per unit volume of cut, w=3.6 mm, a = 0°, t \ 0.06, 0.08, 0.10 mm Q  71  x  3.22 Predicted and experimentally determined cutting energy per unit volume of cut, w=3.6 mm, a = 0°, V : 240, 380, 600 m/min a  72  w  3.23 Predicted cutting temperatures rise in the primary shear zone and the tool-chip interface zone versus cutting speed, w=3.6 mm, a = 0°, t\\ 0.06, 0.08, 0.10 0  mm  74 ix  3.24 Predicted cutting temperatures rise in the primary shear zone and the tool-chip interface zone versus undeformed chip thickness t-i, w=3.6 mm, a = 0°, V : a  w  240, 380, 600 m/min  75  3.25 Plot of predicted cutting temperatures T B and T ; A  nteP  and experimentally mea-  sured wear rate versus cutting speed, w=5.0 mm, a = 0°, £1: 0.06 mm  77  a  3.26 Predicted and experimental measured cutting forces versus cutting speed, w=3.6 mm, a = 0°,ii: 0.06,0.08,0.10mm  78  0  3.27 Predicted and experimentally measured cutting forces versus undeformed chip thickness t  u  w=3.6 mm, a = 0°, V : 240, 380, 600 m/min 0  79  w  3.28 Predicted and experimentally evaluated shear stress in the primary shear zone versus cutting speed, w=3.6 mm, a = 0°, ii: 0.06, 0.08, 0.10 mm  81  a  3.29 Predicted and experimentally evaluated shear stress in the primary shear zone versus undeformed chip thickness ti, w=3.6 mm, a = 0°, V : 240, 380, 600 Q  w  m/min  82  4.1  A proposed chip formation model for cutting with chamfered tools  87  4.2  A proposed slip-line field for cutting with chamfered tools  91  4.3  A generalized prediction algorithm for cutting with chamfered tools  96  4.4  A procedure to estimate cutting temperatures for cutting with chamfered tools..  98  4.5  Effect of chamfer angle on the predicted and experimental shear angles <f> (a), (c)) and predicted friction angles 8 (b), (d) (S10 chamfered carbide tools). . . . 103  4.6  Effect of chamfer angle cti on the total cutting forces ((a), (b), (c), (d) and chamfer forces ((e), (f)) (S10 chamfered carbide tools)  4.7  105  Effect of chamfer angle ai on the cutting temperature (TAB, Ti ) (a), (b) and nter  energy (E ) (c), (d), (S10 chamfered carbide tools) c  x  107  4.8  Effect of cutting speed on the predicted and experimental shear angle <f> (a) and predicted friction angle 8 (b) (MB820 CBN chamfered tools)  4.9  109  Effect of cutting speed V on the total cutting forces ((a), (b)) and chamfer w  forces (c) (MB820 CBN chamfered tools)  110  4.10 Effect of cutting speed V on the predicted cutting temperature in the primary w  shear and the tool-chip interface zones ((a), (b)), the predicted and experimental cutting energy (c) (MB820 CBN chamfered tools)  112  4.11 Comparison of tool wear Vg for chamfered carbide (a), (b), and CBN (c) tools from machining tests  113  4.12 Comparison of tool wear history between a chamfered tool with —15° chamfer angle and a conventional sharp tool (SANDVIK carbide tools)  115  4.13 Comparison of the tool wear history between a chamfered tool with —15° chamfer angle and a conventional sharp tool (SANDVIK carbide tools)  117  C.l  Experimental identification of edge force components  128  C.2  Plot of variation of edge forces with cutting speed  129  xi  Acknowledgement  I would like to take this opportunity to express my sincere appreciation to Professor Yusuf Altintas, my research supervisor, for the most valuable guidance and the financial support throughout the entire research work. My thanks are also due to all my colleagues in the Manufacturing Automation laboratory at UBC for their assistances, encouragements and friendship. I am grateful to Mr. Mashine and MITSUBISHI Material Corporation, Japan, for their kindness to provide CBN cutting tools and the tool holder. Finally, I would like to deeply thank my parents and my wife, xiaochun, for their love and steady encouragement during the course of my work. This work is fully dedicated to them.  xii  Nomenclature  ct  0  main rake angle of cutting tool (degree) chamfer angle (second rake angle) (degree)  Kf  length of chamfer cutting edge (mm)  B  friction angle at the tool-chip interface (degree) shear angle (degree) undeformed chip thickness (mm)  w  width of cut ( mm) contact length along the tool-chip interface (mm)  v  w  cutting speed (m/min.)  v  shear velocity (velocity discontinuity) (m/min.)  Vc  chip velocity (m/min.)  F  shear force acting on slip-line AB (N)  F  total cutting force (tangential force) (N)  F  total feed force (thrust force) (N)  F -cf  chamfer force component in cutting direction (N)  F -cf  chamfer force component in feed direction (N)  R  resultant force exerted on slip-line AB (N)  o-i  flow stresss corresponding strain e = 1.0  n  strain hardening index  T  initial temperature of work material (°C)  a  s  c  t  c  t  s  - room 1  TAB  temperature rise in the primary shear zone (°C)  Tc,  temperature rise in the chamfered edge zone (°C) xiii  Tinter  temperature rise at the tool-chip interface (°C)  Tmod  velocity modified temperature (K)  k B  shearflowstress in the primary shear zone (N/mm )  k f  shearflowstress in the chamfered edge zone (N/mm )  &inter  flow stress acting at the tool-chip interface (N/mm )  lAB  shear strain in the primary shear zone  JAB  shear strain rate in the primary shear zone (1/second)  cf  strain in the chamfered edge zone  ef  strain rate in chamfered edge zone (1/second)  Winter  shear strain rate at the tool-chip interface (1/second)  E  energy dissipation in the primary shear deformation zone (J/mm )  Ef  energy per unit volume in the chamfered edge zone (J/mm )  Einter  energy per unit volume in the tool-chip interface zone (J/mm )  E  total cutting energy per unit volume (J/mm )  P  density of material (kg/m )  c  specific heat of work material (J/Kg° C)  K  thermal conductivity of work material (J/mS ° C)  A  C  e  c  2  2  2  3  3  c  3  3  3  c  3  xiv  To my daughter, Deanna  xv  Chapter 1  Introduction  Dies and molds are used in mass production of plastic parts and sheet metal products using forming technology. Various hardened tool steels are used as die materials. In general, the hardness of a tool steel ranges from 30Rc up to 62 Rc depending on the die application. P20 mold steel, which has an average of 35 Rc hardness, is the most widely used as an injection mold material. The molten plastic is injected into a mold, which has the shape of plastic part to be manufactured in massive quantity. Molds are either machined directly from P20 blanks, or chemically eroded using male electrodes. First, male graphite or copper electrodes are milled on special CNC electrode machining centers. Later, the electrode is penetrated into the blank P20 by gradually eroding the work material. Several trials may be necessary until correct mold dimensions are obtained using electrochemical machining process. The current trend is to replace costly and environmentally unfriendly electrochemical machining by direct high speed machining of molds from steel blanks [4]. High speed machining of hardened tool steels has several constraints. The machine tools must have rigid structures, high speed feed and spindles drives and accurate high speed positioning and contouring capability. The current trend in machine tool design is to develop lightweight machine tool drives using linear motor and electro-spindle technology. Likewise, CNC systems, which have high speed computation as well as contouring capabilities, are developed. In parallel to high speed machine tool design, cutting tool material, geometry as well as process design for high speed material removal are also subject of present research. In this thesis, the focus is placed on the analytical modeling of high speed machining processes. The  1  Chapter 1. Introduction  2  objective is to identify optimal cutting tool geometry and cutting conditions for a given set of work material, and cutting tool geometry and grade. In machining, the material is separated from the blank by forming chips. The deformation starts at the primary shear zone, where the undeformed work material experiences severe strain at high strain rates. The stress and temperature depends on the thermoplastic properties of the work material, as well as the cutting tool geometry and cutting conditions. The shear stress in the shear plane depends on the hardness of the material, as well as its flow stress characteristics, which are dependent on the local strain, strain rate and temperature. Higher the material hardness is, higher the stress and temperature will be at the shear zone. Later the deformed material, i.e the chip, travels over the rake face of the cutting tool, thus imparting more deformation and energy to the chip formation process. The chamfered cutting tools are often used in order to strengthen the cutting edges in high speed machining of hardened materials. Some of the deformed material is trapped over the chamfered zone, acting as a protective thermal and mechanical barrier for the cutting tool. Excessive chamfer angles and cutting speeds increase both stress and temperature loading of the cutting tool, which leads to promoter chipping or accelerated tool wear. Optimal selection of chamfer angle and cutting speed is usually evaluated from costly experimental observations. In this thesis, an analytical model of the machining process with chamfered cutting tools is presented. The model allows analytical evaluation of optimal chamfer angle and cutting conditions (i.e. cutting speed) as opposed to costly experimental trials and guesses. Henceforth the thesis is organized as follows. The literature related to mechanics of cutting, the influence of cutting edge, and cutting conditions on cutting process is reviewed in chapter 2. Chapter 3 presents the mechanics of machining with conventional sharp tools based on the slip line model of Oxley et al. [36]. However, the flow stress properties of the material is evaluated from orthogonal cutting tests as opposed to high speed compression and tensile tests conducted in the past. The model developed in chapter 3 predicts shear angle, cutting forces  Chapter 1. Introduction  3  and temperature for a given set of cutting conditions and tool geometry. The chamfered cutting tool is considered in chapter 4, where the slip line field is modified to include the chamfered cutting edge zone. The primary and secondary deformation zones are modeled similar to sharp tools. The chamfered zone is considered to have a dead metal trapped over the chamfered edge. The chamfered edge zone is treated like an extrusion process, where the dead metal boundary acts like a die surface. The strain, strain rate and temperature dependent stresses in the three deformation zones are modeled, and the total cutting energy consumed is evaluated. By applying the minimum energy principle, the shear angle in the primary shear deformation zone is predicted. The model leads to prediction of stresses, temperature and forces in each zone as a function of chamfer edge geometry, cutting conditions and material properties of mold steel. Optimal chamfer angle and cutting speed, which give the maximum material removal rate at an acceptable cutting tool temperature, are evaluated. The model is verified by high-speed orthogonal turning of P20 mold steel with chamfered ISO S10 carbide and CBN cutting tools. The optimal chamfer angle has been identified as -15 degrees, and the optimal speeds are about 240m/min for ISO S10 and 500 m/min for CBN cutting tools. Thefindingsare supported by tool wear tests conducted at various speeds with different tool chamfer angles. The thesis is concluded with a summary of contributions and future research work in chapter 5.  Chapter 2 Literature Review  2.1  Introduction Machining is one of the most common manufacturing processes used in industry. Mechanics  of machining process aims at understanding the nature of interaction between cutting tools and work materials. This chapter covers the past and current research and development in the mechanics of orthogonal machining process. As seen infigure2.1, the machining process is defined as an operation in which a thin layer of work material, namely, chip, is removed by a wedge-shaped cutting tool from the bulk of work material. A new work surface is formed during machining. Essentially, machining is a process of chip formation. To understand the machining process, it has been usual to simplify the tool geometry from the three dimensional (oblique) geometry to a two dimensional geometry (orthogonal). In orthogonal cutting, the straight cutting edge of the tool is perpendicular to the direction of relative motion between the tool and workpiece. Width of cut w is usually much larger than the undeformed chip thickness ti. The removed chip is formed under approximately plane strain conditions.  Orthogonal cutting is approximately a steady-state process if the  continuous chip is formed during machining. In general, machining process is influenced by: • Material properties • Strain and strain rate • Tool geometry, tool material, and temperature  Chapter 2. Literature Review  Figure 2.1: Diagram of orthogonal cutting  5  6  Chapter 2. Literature Review  During machining, the chip is formed by shearing. The whole volume of metal removed is plastically deformed, undergoing large strain and high strain rate. Thus, a large amount of energy is required to form the chip and move it across the tool face. Understanding the chip formation is essential to the problems associated with the rate of metal removal and tool performance.  2.2  Mechanics of Orthogonal Machining with Sharp Edge Tools  2.2.1  Classical Shear Plane Models  Much research effort has been made in understanding the chip formation since the shear plane model was proposed by Ernst and Merchant [21]. In Merchant's model, the shear stress is assumed to be invariant with shear angle and is distributed uniformly along shear plane. Chip is formed continuously without a built-up edge. Chip is formed as the result of plastic shear deformation along a plane ahead of the cutting edge. Work velocity is instantaneously changed to the chip velocity. This requires a velocity discontinuity in the direction along the shear plane. From figure 2.2, chip ratio r is determined by c  t\ t 2  sincj) cos((f> - ct )  (2.1)  0  Where <f> is shear angle, a is rake angle of tool, 11 is undeformed chip thickness, and t is the 0  2  deformed chip thickness. From equation 2.1, shear angle <j> can be found by measuring chip ratio r . c  (2.2)  tan <f>=-r COSOL — r sma c  0  c  0  Cutting forces are not only associated with the energy input in the machining process, but also they affect the surface finish and tool life. Therefore, it is important to determine the cutting  7  Chapter 2. Literature Review  Figure 2.2: Force diagram in Merchant's model forces required for the given chip load and tool geometry. The cutting forces, tool and chip geometry were related in Merchant's model as seen in figure 2.2. In Merchant's model, cutting force F and feed force F are determined if the shear angle <f>, friction angle 3, shear stress r , c  t  tool rake angle a , and chip load ti, w are known. 0  F  c  =  F  =  ' " " ^ - ^  simp cosO  sinq> cosd 8 = <j) + 3 - a t  0  (2.3) (2.  4)  (2.5)  where 8 defines a angle between resultant force R, and shear plane. Assuming ideal plastic work material, Merchant proposed a shear angle solution using minimum energy method. The  Chapter 2. Literature Review  8  cutting energy per unit volume W is found by c  F V  W  c  =  (2.6)  tiwr d j. cos(8 — ct ) ^ t\w d<j> sincj)cos((f> + 8 — a )  dW _ d(j) c  0  0  cos(8 — a )cos(2(j) + 3 — <x ) _ sin (j) cos (cj) + 3 — a ) 0  2  0  2  a  2<t> + B-a  = 1  0  (2.8)  Which yields to Merchant's shear angle prediction  Quantitatively, this equation has been observed to overestimate shear angles. However, as Turkovitch [18] suggested, shear angle solution 2.9 proposed by Merchant provides a reference for checking other solutions. Lee and Shaffer[22] developed a model which gives cutting forces, the chip thickness, and chip formation from tool geometry, the relevant coefficients of friction, andflowstress of work material. Again, continuous chip formation and sharp tool were assumed. Their model applies theory of ideal plastic deformation without work hardening. Figure 2.3 shows slip line field postulated by Lee and Shaffer. Since slip lines parallel to AC are straight, the stress distribution is uniform in the region ABC. There is no stress transmitted above AB, which a is free stress 7T surface. AC, the shear plane is inclined at — with AB. From Mohr circle and geometrical relationship, the shear angle equation is  V +P = \ <f> = rj + a  0  (2-10)  = ^-(3-a ) 0  (2.11)  Chapter 2. Literature Review  9  Figure 2.3: Chip formation model proposed by Lee and Shaffer [22] Albrecht [32] first realized that ploughing process around cutting edge exists as a secondary mechanism during cutting beside the shear process. He pointed out that any fresh tool has only finite sharpness. Edge forces due to ploughing process have no contribution to shear process in the chip formation. Albrecht proposed a new force diagram of the orthogonal cutting process as seen in figure 2.4. In Albrecht's work, the effect of cutting speed on cutting forces were analyzed. He suggested that only ploughing force P is affected by the cutting speed. As cutting speed increases, cutting forces decrease due to the the decrease of ploughing forces and absence of the built-up edge. Armarego [33] generalized a computer based modelling for the estimation of machining characteristics, such as forces and power. He suggested that forces arise from two sources, that is, work material deformation and edge effect. Cutting force coefficients are determined from the thin shear zone analysis. The " edge " force components are found from machining  Chapter 2. Literature Review  10  Figure 2.4: Force diagram of orthogonal cutting proposed by Albrecht [32] experiments by extrapolating measured cutting forces at zero undeformed chip thickness. The mechanics of orthogonal cutting can be extended to analyze more complex machining process. To model a relative complex machining process, such as milling, Budak, Altintas and Armarego [1] proposed a unify model to determine the cutting coefficients for milling process from the orthogonal cutting test data in order to obtain elemental force components.  2.2.2  O x l e y ' s Shear Zone M o d e l  Metal cutting is a highly complicated process. The flow stress of metals varies with strain, strain rate, and temperature when materials undergo a large plastic deformation. The classical shear plane models fail to explain how flow stress of plastic deformation and frictional state along the tool-chip interface are influenced with variations in the cutting speed. Furthermore, the important characteristics, such as cutting temperatures, the variation of strain rate under  Chapter 2. Literature Review  11  different cutting conditions, can not be analyzed from the classical machining theories, for instance, such as Merchant's model [21]. Oxley and his colleagues [6] developed a shear zone model applying the plastic theory to the analysis of chip formation. Flow stress of work material varies with strain, strain rate, temperature, and the frictional conditions at the tool-chip interface described in terms of the shear flow stress in the layer of chip material adjacent to the tool rake face. The shear zone model they proposed can account for the influence of cutting conditions and work material properties on the important variables in machining, such as cutting forces and cutting temperatures. The chip formation model proposed by Oxley and his coworkers can be represented as shown in figure 2.5. Their theory is based on a chip formation model derived from the analysis of experimental flow fields. Plane strain, steady-state cutting conditions with continuous chip formation are assumed to apply and cutting tool is assumed to be perfectly sharp. Hence, Plastic zone mainly consists of the primary shear zone and secondary deformation zone at the tool-chip interface. AB is a slip-line which represents the direction of maximum shear strain rate and maximum shear stress. Based on the experimental observation, Oxley et al. [7] suggested that the maximum shear strain rate can be estimated from  (2.12)  JAB  where V„ is the shear velocity, IAB is the length of AB, and S is a constant. In the secondary C  deformation zone, a flow zone exists along the tool-chip interface and around the cutting edge due to high compressive stress applied at the rake face-chip interface. Sticking friction is assumed to prevail inside secondary deformation zone. Then the shear strain rate in tool-chip interface zone is given by  (2.13)  Winter —  s • t  2  er 2. Literature Review  Figure 2.5: Chip formation model proposed by Oxley and his coworkers  Chapter 2. Literature Review  13  where 8 is the ratio of the average thickness of interface plastic zone to the chip thickness t . 2  V is chip velocity. The governing equation of stress and strain in the primary shear zone is c  determined by applying the " power law ".  a = <r e  (2.14)  n  x  where <7i and e are effective plastic stress and effective plastic strain, n represents the strain hardening exponent. To account for the effects of strain rate and cutting temperatures, velocity modified temperature which was first suggested by Macgregor and Fisher [20] was introduced to combine the effects of strain rate and temperature on the variation of flow stress. Velocity modified temperature T d can be expressed as mo  T  mod  = {T  + 27Z.O)[l-ulog (e)} 10  (2.15)  where T is cutting temperature (° C) rise in plastic deformation zone, e is strain rate, v is material constant. Oxley [6] suggested that for a given strain, the flow stress a\ and strain hardening index n for a particular work material can be assumed to be a unique function of velocity modified temperature T *. Essentially, a\ and n should be obtained for a wide range mo<  of strain rate and temperature. High speed compression test by Oyane et al. [16] provided a very wide range of temperature (0 ~ 1100 °C) with constant strain rate (450 1/s). Hastings, Mathew, and Oxley applied Oyane's test data to obtain the correlation of flow stress and strain hardening exponent with velocity modified temperature. Although they determined the flow stress under a high speed compression tests which do not cover high strains and strain rates observed in machining, their work is the most fundamental approach in modeling the machining process based on the laws of plasticity. Through the analysis of chip formation, calculating temperature rise in plastic deformation zone is an important aspect since it changes the material properties and influences tool life  14  Chapter 2. Literature Review  directly. Stephenson [37] pointed out that model of Loewen and Shaw [39], the model of Boothroyd [19] as modified by Oxley and his coworkers, et.al. are well known among others in the study of temperature distribution in cutting process. Models they proposed are all based on the assumption of shear plane idealization and cutting with sharp tool. Figure 2.6 shows heat sources on the shear plane and tool rake face. Cutting energy is converted into heat due to plastic work. A, Q represents a portion of heat which flows into work material and (1 — A,) Q a  a  stands for the amount of heat flowing into the chip. Similarly, a portion of heat flows into chip and another portion of heat flows into cutting tool due to friction occurred at tool-chip interface. The rate of energy consumed during cutting is given by W = FV c  C  (2.16)  W  The energy is transformed as heat into two main regions, namely, the primary shear zone, and the secondary deformation zone at the tool-chip interface. The plastic work done W on shear 3  plane is the product of shear force F and shear velocity s  - rr \  F  W, = F.V, =  V  a  cos(<p -  (2-1?)  a) 0  The temperature rise in the primary shear zone is found by adding initial temperature  T  ROOM  in work material to a portion of heat generated by the plastic deformation occurred in primary shear zone T  - T  , „ (1 r  \s)F cosa s  0  J-AB = J-room +m — pctiWcos(<p — a )  -J  (2.18)  0  Where A, and r] are the proportion of heat conducted into work material and a factor which defines the amount of heat converted from plastic work, respectively, p and c are material density specific heat, respectively. The average temperature rise at the tool-chip interface is determined by summing up the temperature rise in primary shear zone TAB and the maximum temperature A TM rise at the tool-chip interface. T  INTER  = T B+i>AT A  M  0<V><1.0  (2.19)  15  Chapter 2. Literature Review  Figure 2.6: Heat Sources in Cutting Process  Again, tp is a factor to allow for possible variations of temperature along the interface. For a given tool rake angle ct , undeformed thickness t\, the cutting speed V , cutting forces can 0  w  be estimated provided the correlation of flow stress of work material with velocity modified temperature is known. Once shear angle <f> is given, then force components applied to cutting are determined from following geometrical force equations  F, cosd  R,  hw sincf) cosd  F  k  fc  A  B  = R sinB s  Fnc = R cos6 a  (2.20)  F = R, cos(8 - ct ) c  0  F = R, sin(3 - a ) k B h w F, sine t  0  A  where k B is shear flow stress acting on slip-line AB. The procedures for predicting cutting A  Chapter 2. Literature Review  16  forces and cutting temperatures, etc. will be discussed in more detail in chapter 3.  2.3  Mechanics of Orthogonal Cutting with Chamfered Edge Tools In the literature, the investigation on tool geometry mainly consists of two categories.  One is the tool edge geometry, and the other emphasizes on the tool rake geometry, such as restricted contact length tools. This section presents some investigative work on the effect of tool geometry on the machining process.  2.3.1  The Effect of Tool Edge Geometry on the Cutting Process  As M.C. Shaw [39] pointed out, Klopstock was thefirstto show that tool life and cutting forces could be altered by restricting the contact length between the tool and chip. K.Hitomi [46] reported that Hoshi invented the " silver-white " chip cutting method (SWC) as seen in figure 2.7. SWC edge is designed with negative rake angle to provide chamfered edge, and a positive rake angle as main rake face. A chip former is provided in the case of the turning tool in order to control the chip. The chamfer traps the work material over the chamfered edge, and the formed dead metal acts like a cutting edge which increases the tool edge strength and reduces tool wear. Figure 2.8 shows chip formation with SWC tool. Hosi [15] suggested that SWC tool performs a unique cutting mechanism involving the controlled built-up edge, and it offers increased tool edge strength, freedom from chip adhesion. E. Usui, K. KiKuchi and K. Hoshi [49] first attempted to model cutting with the cut away tool (artificially controlled tool-chip contact length tool). They applied the theory of ideal plastic deformation material to postulate the plasticflowfields which consist of one centre-fan and two straight slip-line fields. Based on the characteristics of slip-linefields,a quantitative formula was obtained to determine the coefficient of friction on the rake face with artificial  Chapter 2. Literature Review  17  Figure 2.7: Mechanism of SWC cutting restriction of the tool-chip contact length. S. Jacobson and P. Wallen [47] investigated the dead metal zone with different edge geometry. From their experimental evidence, they found that the chamfered cutting edge is almost completely filled by a dead metal zone. They suggested that the relative motion between chip and tool is under the condition of seizure, thus, the secondary shear occurs inside the chip, and the work material adjacent to the chamfer is stagnated. A dead metal zone is formed as a result. M. Hirao, J. Tlusty, et al. [3] observed the same mechanism from their machining tests. They found that a dead metal forms over the chamfer which acts as a cutting edge, and the chip is formed essentially the same way as compared to cutting with and without chamfer, but, the forces are different. They reported that the chamfer has more influence on the thrust (feed) force than the tangential force.  Chapter 2. Literature Review  Figure 2.8: Cross-section of the end of planer chip cutting with SWC tool [15]  18  Chapter 2. Literature Review  2.3.2  19  Zhang's T h r e e Zone M o d e l  H.T. Zhang, P.D. Liu and R.S. Hu [50] analyzed the mechanics of machining with chamfered tools by considering the primary, dead metal and the secondary deformation zones separately. Their model predicts shear angle in orthogonal machining with chamfered tools. Based on their experimental observations using microphotographic and quick-stop techniques, it is found that the existence of dead metal zone is not dependent on the cutting speed, tool main rake angle or the chamfer angle. They concluded that the decrease of shear angle due to chamfer is about 2° ~ 3° compared to that for cutting with sharp tools under same cutting conditions.  2.3.3  Summary  The major shortcoming of classical shear plane models is that strain hardening, strain rate sensitivity, and thermo-mechanical coupling are neglected. It is essential for high speed machining to analyze these important features. The "shear zone " model proposed by Oxley et al. [6] included these effects in a model giving more realistic explanation. Their model only considered machining with sharp tools and required flow stress of material from high speed compression tests. Finite element method by Strenkowski and Carroll [56], Komvpoulos and Erpenbeck [57], and Ortiz and Marusich [58] can describe the temperature, stress and strain rate distribution in more detail. However finite element modeling of machining process requires intensive computation time and problems associated with the criterion of elemental node separation and modeling of the tool-chip interface due to large deformation are still difficult to solve at the present stage.  The past work reported on the mechanics of machining with chamfered tools was mainly experimental, and lacked the support of an analytical model. In this thesis a comprehensive analytical model of the process is developed as shown in the following chapters.  Chapter 3  M o d e l i n g of Machining with Sharp Tools  3.1  Introduction  Mechanics of machining aims to investigate how process variables, such as cutting forces, power, and temperature etc., vary with the machining conditions and materials properties. In this chapter, a mechanics model for the machining with conventional sharp tools is presented. Strain, strain rate, temperature and stress are evaluated based on the model proposed by Oxley et al. [6], [36]. The flow stress of work material under high strain rate and temperature is modeled through orthogonal machining tests with S10 carbide sharp tools on P20 mold steel. A minimum energy method is proposed to predict shear angle from given cutting conditions. Hence, the model developed in this chapter focuses on the plastic deformation in two main areas, namely, the primary shear and the secondary deformation (tool-chip interface zone) zones. Energy dissipation involved in these two regions are formulated. In the predictions of cutting forces, the analysis of edge forces is incorporated. To compare the predictions by this model, orthogonal cutting tests have been performed. Through analysis, steady-state cutting with continuous chip formation, sharp edge tool, and plane strain are assumed.  3.2  Modeling of Plastic Deformation  3.2.1  in Cutting with Sharp  Tools  Stress a n d Strain  For plane strain problems, the plastic flow is parallel to the xy plane, and velocity field is independent of Z direction. Figure 3.1 shows the state of stresses bounded by slip-lines. 20  21  Chapter 3. Modeling of Machining with Sharp Tools  P Physical Plane  Stress Plane in Mohr's circle  Figure 3.1: State of stresses in plane plastic flow Through each point in the plane of plastic flow, a pair of orthogonal curves along which the shear stress has its maximum value k. These curves are called slip-lines denoted by SL and a  SL/3 lines. The families of slip-lines represent the direction of maximum shear stress and maximum shear strain rate at every point in the plastic deformation region. The stress acting on the slip-lines is shear stress k and the normal stress on the slip-lines is hydrostatic stress p . The state of stresses at a point is completely determined if p and k and orientation of slip-lines are known. The work material is assumed to be isotropic. The components of stress depend only on x  22  Chapter 3. Modeling of Machining with Sharp Tools  and y. Txz  = T  =  yz  0  (3.1)  The Levy-Mise stress-strain increment equations [59] are expressed as = <^'ciA = ( ? ) ( * ) * . /  den  (3.2)  6 <T deij  -  (<Tij  — <r )<iA  where  m  cr = ^  ——  y  x  m  (3-3)  o  de, = ( -)d\{*  i^±fA  -  2  2  (3.4)  }  where cr;/ is the deviator stress tensor and dX is a scalar non-negative constant of proportionality which is not material constant and may vary throughout the stress history. The z direction is a principle direction. Thus, cr is a principle stress. For the plane strain problem, strain and shear z  stress related in Z direction show =  =0  = lyz  Ixz  (3.5)  Therefore de  z  = d~j = d-y xz  yz  = 0  (3.6)  From equation 3.4, o~ and hydrostatic stress are obtained z  (o- + (Ty)  (3.7)  x  2 Cm =  fax  + (T + <T )  (3.8)  Z  y  3 {<T* + O-y +  + <Ty)}  3 (q-x + (Ty)  2 <7  =  2  <7  m  =p  (3.9)  Applying Von Mise yield criterion for plane strain plastic deformation gives (<T - o-y)  2  X  + (o-y - <T ) + (o2  Z  - <T ) + Q( 2  z  X  2 TXY  +  2 T Y Z  +r  2 z x  ) =  6k  2  (3.10)  23  Chapter 3. Modeling of Machining with Sharp Tools  where k is the yield stress in pure shear. Equation 3.10 reduces to  (cr - * ) + \ r 2  x  y  = 4k  2 x  (3.11)  2  In the absence of body forces, the equations of equilibrium for quasi-static deformation for plane strain problem are  do- ^ dr dx dy dr d(T dx dy x  xy  xy  y  =  0 (3.12)  = 0  From Mohr's circle as shown in figure 3.1, the yield criterion is satisfied by cr = —p — ksin2^> x  o-y = — p + ksin2^>  r  xy  (3.13)  = k cos 2d>  Substituting equation 3.13 into the equilibrium equations 3.12 and differentiating and collecting terms gives ^ - + 2k cos 2d>^- + 2k sin 2<f>^-  = 0  ox ox oy dv> . , dd> , , dq> 2k cos 2d>-^- + 2k sin 2i>^- = 0 oy oy ox  (3.14)  The choice of x and y axes are arbitrary, let x and y axes be tangential to the SL and SLp a  shear slip lines direction. Thus, d> is zero. If material is assumed to be perfectly plastic (non-hardening) with constant k, equations 3.14 reduce to 0 along SL line a  OX  OX  (3.15) I  dy  0 along SLp line  dy  Integrating equation 3.15 gives the well known Hencky's equations A p + 2kd> = 0 along SL line a  A p — 2k<t>  =  0 along Slip line  (3.16)  24  Chapter 3. Modeling of Machining with Sharp Tools  Palmer and Oxley [61] proposed a modified Hencky's equation which allows for the variation of yield stress when the work-hardening of the material is taken into account. Again, let the x and y axes be taken along the tangents to the SL  and SLp lines respectively, this corresponds  a  to 6 = 0, yields dp  . „,0k  --i- ox dp  oy  dd dk 2kcos26-^- + cos26nl  stn14>-  ox  nl  ox  M  M  nl  dp  n l  oy  „ , dd>  ox  dk  = 0  oy  nl  oy  nl  oy  • d\a d6 dk + sin2<f>— + 2kcos2d)-^- + cos2<j>nl  . d<f> 2ksin26-^-  . d<t> • 2ksin2<f>-J- - 0 nl  n  ox  „ (3.17)  dp . 86 dk ^dSLp T - - ^ rdSL i dSLp -  „ = 0 along SLp line  n  2  k  0  Equation 3.17 presented by Palmer and Oxley [61] indicates that the variation of hydrostatic stress P along a slip line is not only dependent on the curvature of slip line, but also upon the rate of change on the flow stress of work material in a direction perpendicular to the slip line. Having analyzed the experimental flow field in machining process, Hasting, Mathew and Oxley [36] presented a theory of chip formation. As illustrated in figure 2.5, plastic deformation undergoes in a finite thickness zone in Oxley's shear zone analysis. The plane A B and tool-chip interface are both assumed to be the direction of maximum shear stress and maximum shear strain rate. From equation 3.17, let A B be SL  a  slip line in the primary shear zone. The  variation of hydrostatic stress along AB p and shear flow stress k B are expressed as A  dp dSL  a  . d<f> d k + 2k —— = 0 dSL dSLp A  AB  a  If slip-line AB is assumed a straight line, this leads to  B  ,  ,  (3.18)  25  Chapter 3. Modeling of Machining with Sharp Tools  Then, dp dSL  <9k dSLp  (3.20)  AB  a  The flow stress and strain relation is governed by power law and is expressed as O-AB  N  A  From Von Mise yield criterion, shear flow stress k  , strain rate €AB, and strain e B are  A B  A  °~AB  1  k  (3.21)  = <Ti{e B)  A  B  lAB  CAB  ~  t-AB  (3.22)  ^3  lAB  "  V3  From equation 3.21, the variation of flow stress (TAB with e B can be expressed as A  d(TAB _ deAB  n  °~AB  (3.23)  £AB  Similarly, taking the derivative for equations 3.22 gives ,  &i£AB  n  (3.24)  v/3 rfkAB  do-AB  =  d'iAB  ^( ^) ~ 7s  n =  n  1  \/3  de B A  =  X  W ^ T  n k  =  VSjAB  A  B  lAB  (3.25)  Therefore, the variation of shear flow stress along SLp slip line which is perpendicular to A B can be expressed as the form dfAB  cflc B  <ik B  dSLp  d")AB dt  A  A  dt  dSLp  (3.26)  dt can be determined from velocity diagram as shown in figure d SLf 3.2. Where SLp corresponds to CF or EA if AA'=V dt.  where dt is time interval.  w  EA = AA' sind) = V sin<j> dt w  (3.27)  Chapter 3. Modeling of Machining with Sharp Tools  26  Figure 3.2: Velocity diagram in chip formation Then,  di dSLp  is given by dt  (3.28)  dSL@ V sind> w  Shear strain occurring as work material crosses the slip-line AB is given from geometrical relation shown in figure 3.2. AC__AE^ Fp" ~ ~AE  +  1  CE AE  (3.29) cosa  0  sind>cos(d> — ot. ) 0  Hence, substituting equations 3.28, 3.25 into equation 3.26, the variation of shear flow stress  27  Chapter 3. Modeling of Machining with Sharp Tools  along A B as shown in figure 2.5 is <^AB  dk&B d^AB  dSLp  d'jAB  dt  dt  d S Lp  JAB T}—r—7  IAB AB  _  (3.30)  Vw sin<p  1 V sin6  nk V IAB IAB S nk B s  s  w  A  c  IAB  Note that shear velocity in the primary shear zone V, is given by V  cosct  w  (3.31)  0  cos(<j) — ct ) 0  3.2.2  Plastic Deformation in thePrimary Shear Zone  As seen in figure 2.5, slip-line AB is assumed to be the line of maximum shear strain and shear strain rate as proposed by Oxley et al [6], [36]. For the given undeformed thickness ty, tool rake angle ct , width of cut w, and cutting speed V , shear strain JAB and shear strain rate 0  w  JAB in the primary shear deformation zone are obtained from the following equations cosct  0  IAB  =  sin<j> cos(6 — ct ) V V B  IAB  v„  -  =  IAB -7—  Of V  w  —  s  lAB I  0  s  (3.32)  s  = >~>c I IAB IAB  COSOLQ  J  cos(6„ - ct ) '  A  _  r-i  sin<j) ,  B  0  a  where a , 6 , IAB, V are main rake angle of cutting tool, shear angle, length of shear line AB, Q  S  3  and shear velocity along AB. If shear angle varies between 5° ~ 40°, the average value of strain ^AB ~ 6, i.e. S « 6.0, is obtained from equation 3.32. Where S is designated as an c  c  average value used to calculate shear rate JAB- Oxley et al. [36] observed an average strain value of 5.9 from their experiments. From Von-Mises yield criterion, shear flow stress ( k f i ) distributed along A B in the primary A  Chapter 3. Modeling of Machining with Sharp Tools  28  shear zone is found by °~AB  =  0~\tAB IAB  ,  &AB  F  k  =  S  A B  (3.33)  &1 €AB  IAB W =  — L A B  W  where O~AB, n, and F are flow stress, strain hardening index, and shear force along the slip-line S  AB, respectively. o- and n are found by evaluating the shear stress, shear strain and strain rate x  (equations 3.32 and 3.33) from a set of orthogonal cutting tests. The procedures to obtain GAB and n will be presented in detail later. During machining, the plastic energy dissipated in the primary shear zone is transformed as heat. To determine shear flow stress k  A B  in this zone, temperature, strain rate, and strain  are needed. As proposed by Boothroyd [19] and Oxley et al. [6], [36], temperature rise in the primary shear zone is predicted by rp  _rp  IAB  —  J-room  , (1 ~  \,)F.CQBCt  0  71 d pctiWcos(<p — a )  + n[—:  (3.34)  0  where T , ROOM  p  and c are initial temperate, density, and the specific heat of work material,  respectively. A, and n are the empirical factors, which indicate the partial heat conducted into the work material, and the percentage of the deformation takes place on shear plane (AB), respectively. The values of the constants evaluated from orthogonal cutting tests are given in the Appendix A. Oxley [6] suggested that better estimations of temperature rise in the primary shear zone TAB is obtained when n is taken between 0.75 and 0.95, which is supported by the finite element analysis results reported by Tay et al. [73]. The following sections will show that the iterated procedures for the calculation of the mean temperature in the primary shear zone is required since thermal conductivity « and specific heat c are temperature dependent.  29  Chapter 3. Modeling of Machining with Sharp Tools  The analysis of energy balance is introduced in this model. Unlike Oxley's approach [6], shear angle will be predicted by using minimum energy method instead of graphical method. Energy consumed in machining is composed of two source, namely, energy dissipations in the primary shear deformation and secondary deformation at the tool-chip interface zones. The energy dissipation in the primary shear deformation zone E is determined from the strain s  energy given by  E,  = _  ft™  <rde=-^-(e )  n+1  AB  (3.35)  °~i ° i"+i n + l -\/3 sind>cos(d> — ct ) COSOL  r  0  It can be seen that the energy consumed in the primary shear zone (E , J/mm ) is influenced 3  s  by strain hardening (n), flow stress ( c r i ) , tool rake angle  (a ), Q  and shear angle (d>). "Classical  shear plane" models [21], [22] assumed ideal plastic deformation without strain hardening in the chip formation. Therefore, their models can not account for the effect of strain hardening.  3.2.3  Plastic D e f o r m a t i o n i n t h eT o o l - C h i p Interface  Zone  Chip is formed by the shearing action in shear zone during the machining. Severe friction occurs in the contact area between the chip and the cutting tool. Zorev [28] suggested that the real contact area is equal to the apparent for part of the contact length under most cutting conditions. It was found that sticking friction prevails around the cutting edge and sliding friction occurs around the end of contact area between the tool and the chip. Boothroyd et al. [60] suggested that both the coefficient of sticking friction and the coefficient of sliding friction are constants. The mean coefficient of friction between the tool rake face and the chip is found to be variable, depending on the normal stress distribution on the tool rake face and shear stress at the tool-chip interface. The plastic flow zone of intense shear strain near the tool-chip interface are normally observed [45]. The existing knowledge about stresses distribution at  30  Chapter 3. Modeling of Machining with Sharp Tools  Figure 3.3: Distribution of normal and shear stresses at the tool-chip interface tool-chip interface is not clear. Most of work in the literature is based on the experimental observation using the photo-elastic technique and the slip tool method. In this thesis, the sliding and sticking zones are assumed to be equal to the half of the chip-tool contact length (l ), see figure 3.3. Furthermore, the shear stress is assumed to be c  linearly decreasing from constant shear load at the sliding zone. The chip moves over the tool rake face at chip velocity (V ), causing further plastic deforc  mation which is assumed to occur in a thin work material layer. The shear strain rate within this layer is approximated by Oxley et al. [6], [36] as  (7t„t ) e r  31  Chapter 3. Modeling of Machining with Sharp Tools  v s •t  Kinter  c  —  2  V  sina  w  0  cos(6 — Ct ) t cos(<f> — a )  (3.36)  0  x  tl  0  sin<f>  where V and t are the chip velocity and the chip thickness, respectively. S is the ratio c  2  of thickness of plastic deformation layer at the tool-chip interface to the chip thickness t . 2  The average thickness of the plastic layer is measured from cut chips (P20) with Scanning Electron Microscope (SEM), and found to be about 5% of the measured chip thickness. Same observation was reported by Tay et al. [73] and Stephenson [37]. Severe plastic deformation and friction in the tool-chip interface causes high temperature rise compared to that in the primary shear zone. Tool life is directly affected by the temperature loading in this zone. The analysis of temperature in tool-chip interface zone is included in the model development since flow stress of work material varies with temperature at the toolchip interface. Applying the same approach as proposed by Oxley et al. [6], [36], [73], the temperature rise at the tool-chip interface is determined by  T  = T  INTER  AB  + ^AT  M  0<^<1.0  (3.37)  where ATM is the maximum temperature rise in the chip which occurs at the interface and •0 is a factor which allows for the variations of temperature along the interface. TAB is the temperature evaluated in the primary shear zone. ATM is determined from equations shown in Appendix A. The determination of temperature is considered by assuming heat generated in a finite plastic deformation zone (St ) instead of plane heat source along the tool-chip interface. 2  Noted that an iterative procedure is required in order to calculate temperature rise at the tool-chip interface because thermal properties «, c, are also temperature dependent. The chip-tool contact length (/ ) is required to evaluate the friction energy produced on c  32  Chapter 3. Modeling of Machining with Sharp Tools  the rake face. Gad and Armarego et al. [35] reviewed the literature, and concluded that the most adequate method of contact length estimation is to use empirical models calibrated from machining tests. In this chapter, the contact length (l ) along the tool-chip interface is identified c  from machining tests, where l is calibrated as a function of cutting speed and feedrate. The c  equation will be shown later. Since the stresses distribution along the tool-chip interface is assumed, hence, the area of shear load on the rake face gives the total friction force exerted at the tool-chip interface Ff - k c  where ki  inteT  ^W + i k r  \  inte  is the shear flow stress and equal to k  nter  interface ai  nter  W  =  =  i n t e r  (3.38)  \ Winter h W Winter  . The flow stress at tool-chip  is mapped from the velocity modified temperature T , which is given in mtc  Appendix B. The energy per unit volume dissipated in tool-chip interface zone Ei  nter  is found  by FfcV  c  E,inter  — V t±w w  _  3 k r l wV sitld) 4ti w V cos(d> — ot ) m t e  c  w  w  0  (3.39) _  Winter l wV sin<f) c  w  4\/3 i i w V cos(cj) — a ) w  _  0  Winter h sin<f> ti cos((j> — a ) a  where V is the chip velocity given by equation 3.36. c  3.3  Experimental Modeling This section describes the experimental setup for orthogonal machining of P20 mold steel. A  33  Chapter 3. Modeling of Machining with Sharp Tools  set of orthogonal machining tests have been performed under a wide range of cutting conditions. The chip thickness t , cutting force F , feed force F , and contact length l are measured from 2  c  t  c  experiments. Tool wear tests for cutting with sharp tools also have been conducted. Similar to a transfer function to govern the relation between inputs and outputs of a dynamic system, the correlation of flow stress <7i, flow stress o-i , and strain hardening index n are identified nter  through machining tests. The flow stress of P20 work material under high strain rate and temperature identified from machining with sharp tools is also applied in the modeling of machining with chamfered tools as shown in chapter 4.  Table 3.1: Chemical composition of P20 mold steel  Approximate composition% Standard specification Delivery condition  3.3.1  C 0.37  Si 0.3  M 1.4 n  C 2.0 r  Ni 1.0  M S 0.2 0.08 0  AISI P20 Modified Hardness 321 H B , 35 H R C  E x p e r i m e n t a l Setup  Figure 3.4 shows the schematic representation of the experimental setup used in this thesis. The experimental system consists of P20 workpiece, cutting tools, data acquisition components, and C N C turning center. The work material used in machining tests is P20 mold steel. Table 3.1 and 3.2 show the chemical compositions and general mechanical properties. In the machining tests, P20 work material was made as a disk with outer diameter about 98.90 mm and thickness of 3.6 mm. A l l disk specimens were ground to keep accurate thickness  Chapter 3. Modeling of Machining with Sharp Tools  34  Figure 3.4: Diagram of experimental setup for orthogonal machining of P20 mold steel  35  Chapter 3. Modeling of Machining with Sharp Tools  Table 3.2: Mechanical properties of P20 Mold steel Temperature Density  Kg/m  20° C  Thermal conductivity J/ms°C Modulus of elasticity GPa  Specific heat J/Kg°C  3  200° C  400° C  7800  7750  7700  29.0  29.5  31.0  205  200  185  460  Chapter 3. Modeling of Machining with Sharp Tools  within tolerance of about 5.0 pm.  36  Figure 3.7 shows the dimension of the disk workpiece  prepared for machining tests. The disk workpiece is connected with a shaft by two bolts. The shaft is clamped to the spindle by the collet of machine tool. Figure 3.5 shows the dimension of the shaft used in the experiment. Initially, some disks were made with the average thickness about 5.0 mm for some cutting tests. Blank carbide insert made by S A N D V I K (N151.2-650-50-3B) with grade number S10 were used in the machining tests. This type of tool has the basic geometry as shown in figure 3.8. A l l of them have zero degree rake angle and 10° clearance angle. These tools are prepared as orthogonal cutting with sharp tools. Figure 3.6 shows the Hardinge Super-Precision S U P E R S L A N T C N C turning center. A l l cutting tests have been conducted using the same setup. C N C turning center can be programmed to provide the constant surface speed due to the changes of utter diameter of disk workpiece. For the desired cutting speed, the corresponding spindle speed N is determined by N =  where D (mm) is the diameter of disk workpiece, V  (3.40)  w  (m/min) is the cutting speed. Data  acquisition system consists of a Kisler three component piezo-electric 9257A dynamometer mounted on the turret, 5004 Dual Mode charge amplifiers, DSP external interface box, a P C supported by I M M real time signal processing software, which is developed by Manufacturing Automation Laboratory at University of British Columbia, and NIC-310 digital oscilloscope for signal monitoring.  3.3.2  Experimental Procedures  The orthogonal machining tests have been conducted under the cutting conditions as shown in table 3.3. A conventional parting process was applied with the main cutting edge of the tool set normal to the feed force. This setup makes machining as orthogonal cutting process.  37  Chapter 3. Modeling of Machining with Sharp Tools  4 . 466 3-RIGHT  2-FRONT QTY  f  1 FSCM I REQO [ NO 1  PART OR IDENTIFYING NO  1 1  NOMENCLATURE OR DESCRIPTION PARTS  UNLESS OTHERWISE SPECIFIED DUCNSIONS ARE IN INCHES TOLERANCES ARE: FRACT1ONS DEC1 UALS ANCLES • -XX+ DO NOT SCALE DRAWING YREAVMENY  CONTRACT NO.  APPROVALS  | j  MATERIAL SPECIFICATION  LIST  Designed by H.Ren DATE  TITLE  S h a f t  DRAWN CHECKED  F1N1SM ISSUED SIMILAR TO  ACT.  ft  CALC WT  SIZE FSCM NO.  DWG NO.  A SCALE  |  Figure 3.5: Shaft used in machining tests  | SHEET  | ITEM I NO  38  Chapter 3. Modeling of Machining with Sharp Tools  4 Axis  Figure 3.6: Hardinge C N C turning center used in machining tests  39  Chapter 3. Modeling of Machining with Sharp Tools  1 ] FSCM ) QTY REQD | NO J  PART OR IDENTIFYING NO  1 |  NOMENCLATURE OR DESCRIPTION  1 j  MATERIAL SPECIFICATION  PARTS LIST UNLESS OTHERWISE SPECIFIED DIMENSIONS ARE IN INCHES TOLERANCES ARE: FRACT1ONS OEC1MALS ANGLES + .XX-  CONTRACT NO.  +  CO NOT SCALE DRAWING YREATMENY  APPROVALS  Des i gned by DATE  H.Ren  TITLE  Disk  DRAWN  ( workpiece  )  CHECKED  FlN1SH  ISSUED SIMILAR TO  ACT. WJ CALC VT  SIZE FSCM NO.  DWG NO.  A SCALE  |  Figure 3.7: Workpiece used in machining tests  | SHEET  { ITEM j NO  Chapter 3. Modeling of Machining with Sharp Tools  10.18 mm »  Figure 3.8: S A N D V I K caxbide insert  41  Chapter 3. Modeling of Machining with Sharp Tools  Cutting forces are found by averaging the forces recorded from experiments. The chip-rake face contact length was measured with a tool microscope for each test. The chips are collected, their thicknesses are measured. The weight of chip sample is measured by an electronic scale. Then, chip thickness t is determined by equation 3.41, where h is the length of a small piece 2  of chip sample, p is density of P20 mold steel, and w is the weight of a small piece of chip g  sample, respectively.  Table 3.3: Cutting conditions Cutting speed m/min  Feedrate mm/rev w=3.6 mm  0.02, 0.04, 0.06, 0.08, 0.10  100, 240, 380, 600  w=5.0 mm  0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09  60, 120, 240, 380, 600  w=5.0 mm  0.04  60, 120, 200, 240, 380, 480, 600, 780, 1000, 1200  h = -f*-  (3.41)  phw  Then, experimental shear angle is determined from the calculated chip ratio r  c  r  c  =  4> =  jtan'  (3.42) 1  .  r cosa c  1 —r  0  c  .„  A—  sinct  (3.43) 0  Chapter 3. Modeling of Machining with Sharp Tools  42  Figure 3.9: Illustration of measurement of contact length l and tool wear land V B from the cutting tool c  From experimental cutting force measurement, the mean coefficient of friction at tool-chip interface is given by t a n f j  _ (F - F ) + (F F )tana ~ (F - F ) - (F - F )tana t  te  c  ce  ce  c  t  te  t  { 3 M  0  where F and F are measured cutting force and feed force, F c  0  ce  >  and F are edge force compote  nents in cutting and feed directions, respectively. The detail of the identification of edge force components F  ce  and F  te  is shown in Appendix C.  43  Chapter 3. Modeling of Machining with Sharp Tools  A scar remains on the rake surface of cutting tool due to severe friction acting at the toolchip interface. Cutting tools get worn after certain machining time, which ultimately leads to the breakage of cutting tool. The stress distribution at the tool-chip interface is affected directly by the contact length. In experiments, the contact length l is measured with a tool c  maker microscope. Figure 3.9 illustrates the experimental method to determine the contact length l and tool wear land V B after each cutting test. The correlation of contact length l with c  c  undeformed chip thickness i i and cutting speed V is shown in figure 3.10. It can be seen that w  contact length along the tool-chip interface varies with cutting speed and uncut chip thickness. Based on the experimental observation, the contact length l is estimated from the correlation c  with the cutting speed V and undeformed chip thickness i i . w  l  = 0.2432 - 0.313 x 1 0 K , + 0.47 x l O _8  c  3  - 5  ^  2  -0.00198K, - 2.3499t! + 3.2i, 2  (3.45)  Table 3.4 and 3.5 show the data obtained from machining tests. Next section will demonstrate how to establish the material constitutive relation of flow stress and strain hardening exponent under a range of strain and strain rate from the machining test data. The proposed procedures involve the mapping of flow stress and strain hardening exponent from strain, strain rate, and velocity modified temperature which are obtained from machining tests. It is noted that cutting force FJ and feed Ft shown in table 3.4 and 3.5 are given by subtracting edge forces F and F (see in Appendix C) from the measured total cutting force ce  te  F and feed force F . Figure 3.11 shows variation of shear stress with cutting speed and c  t  undeformed chip thickness. Experimental shear stress k B is calculated from measured forces A  FJ and FJ  (3.46) where d> is experimental shear angle found from equation 3.43.  44  Chapter 3. Modeling of Machining with Sharp Tools  Table 3.4: Machining test data (" sharp tool "), w=3.6 mm  <i (mm) 0.02 0.02 0.02 0.02 0.04 0.04 0.04 0.04 0.06 0.06 0.06 0.06 0.08 0.08 0.08 0.08 0.10 0.10 0.10 0.10  V (m/min) 100.0 240.0 380.0 600.0 100.0 240.0 380.0 600.0 100.0 240.0 380.0 600.0 100.0 240.0 380.0 600.0 100.0 240.0 380.0 600.0 w  F '(N) 125.07 119.91 128.43 149.08 315.08 276.90 304.85 320.98 459.46 414.80 453.88 479.63 592.30 563.98 593.01 633.73 731.82 635.18 730.69 777.73 C  *i'(N) 41.40 27.86 39.99 60.30 147.57 83.020 88.380 161.22 199.20 114.11 135.89 204.18 248.65 159.09 180.29 302.48 302.80 182.30 214.68 314.18  0(rad) l (mm) c  0.236 0.370 0.405 0.433 0.299 0.448 0.495 0.502 0.366 0.511 0.518 0.523 0.420 0.519 0.518 0.534 0.447 0.539 0.551 0.571  0.135 0.095 0.096 0.097 0.194 0.155 0.150 0.179 0.290 0.177 0.185 0.334 0.336 0.230 0.212 0.334 0.410 0.252 0.283 0.430  45  Chapter 3. Modeling of Machining with Sharp Tools  Figure 3.10: Plot of correlation of contact length with cutting speed V and undeformed chip thickness t-i, w=3.6 mm. w  Chapter 3. Modeling of Machining with Sharp Tools  46  Figure 3.11: Plot of correlation of shear stress on the shear plane with cutting speed V and undeformed chip thickness t\, w=3.6 mm.  v  47  Chapter 3. Modeling of Machining with Sharp Tools  Table 3.5: Machining test data (" sharp tool "), w=5.0 mm  ti(mm) 0.04 0.04 0.04 0.04 0.04 0.04 0.04  3.3.3  V (m/min) 60.00 120.0 200.0 240.0 380.0 480.0 600.0 w  iV(N) 632.44 530.14 447.64 416.00 448.20 396.33 520.90  F '(N) 381.82 352.42 233.00 208.29 140.20 117.50 204.10 t  ^>(rad) 0.257 0.425 0.488 0.497 0.527 0.537 0.540  l (mm) 0.370 0.196 0.129 0.114 0.118 0.124 0.132 c  Modeling of Flow Stresses and Strain Hardening Under High Strain Rate and Temperature Through Machining Tests  When applying "shear zone " model proposed by Oxley et al. [6], [36], a reliable material constitutive equation is required. The flow stress of work material obtained from high speed compression tests was used in Oxley's model. This section presents a method to model the flow stresses in the primary shear and secondary deformation zones in detail. A number of C programs were developed to facilitate this effort. From machining test data shown in tables 3.4 and 3.5, shear angles, mean friction coefficients at the tool-chip interface, and shear stresses in the primary shear and the tool-chip interface zones are evaluated and the corresponding strain rate and temperature are evaluated as well. Hence, empirical constitutive equations for P20 work material are obtained. The procedures are summarized as follows: • Input a cutting test data file, which contains given undeformed chip thickness ti (mm), cutting speed V (m/min), cutting forces F ' and F ' (N), shear angle d> (rad), and measured w  contact length l (mm). c  c  t  Chapter 3. Modeling of Machining with Sharp Tools  48  • Calculate the shear strain JAB and shear strain rate JAB in the primary shear zone, using equation 3.32. • Calculate the shear strain rate 7;„t in the tool-chip interface zone, using equation 3.36. er  • Calculate temperature rise in the primary shear zone T B and in the tool-chip interface A  zone Ti ter shown in Appendix A . n  • Determine the mean friction coefficient at the tool-chip interface tan(0), angle (8) between resultant force R and slip-line AB, and strain hardening index n. s  • Calculate shear stress k/vB, and then <ri is found from equations 3.33. • Calculate shear stress k i  n t e r  acting along the tool-chip interface.  The mean friction angle 3 is determined by 0 = a + tan' ^) 1  (3.47)  0  where F ' and F ' are the cutting and feed forces, which are obtained by subtracting the edge c  t  forces from the measured cutting and feed forces. The angle 9 which indicates the angle between the resultant force R and slip-line AB in the primary shear zone as seen infigure2.5 s  is found from equation 6 = 6 + 3 -  a  (3.48)  0  As shown previously in equation 3.20, the variation of hydrostatic stress p along slip line AB in figure 2.5 is  A  p  P A - P B  = tlg  A 5 I  =  5  f ^  A  i  ° «  (3  -  49)  ( - °) 3  5  49  Chapter 3. Modeling of Machining with Sharp Tools  Palmer and Oxley [61] analyzed the slip-line along AB and they suggested that this slip-line must in fact bend near the free surface at 45°. From Hencky's equation 3.16, this yields PA = k  A  B  [l +  2(^-^)]  (3.51)  From geometrical relation as shown in figure 2.5, 9 is given by t a n Q  =  F ^ F  (PA + P B ) / 2  =  ( 3  5 2 )  K B  s  A  According to the theory proposed by Oxley et al. [6], substituting equations 3.50, 3.51, and 3.30 into equation 3.52 gives tanO = [1 + 2<J - *)] 4  5  ;f . = [1 + < - 4)] - ^ llAB KAB 4 ^ A  B  i  j  B  (3.53)  where S « 6.0 and IAB is length of AB given by C  IAB =  (3.54)  sinq>  From equation 3.53, the average strain hardening index n in the primary shear zone is obtained >  =  ,! + » ( } - « - « " » ] •  (3.55)  Sc  To determine the cutting temperature in the primary shear zone and the secondary deformation zone at the tool-chip interface, an iterative procedure is again applied to calculate cutting temperatures TAB and T j  since material properties, such as specific heat c and thermal  n t e r  conductivity K, are temperature dependent. Figure 3.12 shows an algorithm to evaluate cutting temperature  TB A  and T  .  INTER  T  ROOM  is the initial temperature of work material or room tempera-  ture. The coefficient A, is determined from equations shown in Appendix A . The evaluation of temperature on the shear plane and the tool-chip interface zone is carried out using experimentally identified shear angle (d>), shear stress ( k A B ) , and friction coefficient (tanB). As proposed by Oxley and his coworkers [6], velocity modified temperature T d is introduced to combine mo  Chapter 3. Modeling of Machining with Sharp Tools  Inputs:  11,  ao, n, Xs,  50  W, Troom, F s , Ffc, <(>,  Initialize: TAB =  I room  7  \\f  Temperature rise in primary shear zone • Calculate specific heat c and thermal conductivity K .(for P20  mold steel)  K = 28.740 + 0.0053 T AB ; pc = 3.59E+06 - 100.0 TAB • Calculate TAB TAB = T r o o m •  r  (1  -  Xs)  F s C O S  0 C  o  ]  ^ Lp c ti w cos( < > - a )J o  new TAB - old TAB< 1 TAB = new TAB new TAB - old TAB> 1  Compare new TAB and old TAB  Initialize  Timer=  Output TAB  TAB  Temperature rise at tool - chip interface • Calculate secific heat c and thermal conductivity K K = 28.740 + 0.0053 Timer ; p c = 3.59E+06 -100.0 Timer; Timer = TAB + \|/ AT M  Timer = new  new  Timer  Timer - O l d Tinter > 1  neW  Compare new and  old  Timer - O l d Timer < 1  I inter  Timer  Output  Timer  Figure 3.12: A n algorithm of the cutting temperature estimation  Chapter 3. Modeling of Machining with Sharp Tools  51  Table 3.6: Flow stress c r strain hardening index n, cutting temperature TAB obtained from machining test data 1?  tl  (mm) 0.02 0.02 0.02 0.02 0.04 0.04 0.04 0.04 0.06 0.06 0.06 0.06 0.08 0.08 0.08 0.08 0.10 0.10 0.10 0.10  v  w (m/min) r  100.0 240.0 380.0 600.0 100.0 240.0 380.0 600.0 100.0 240.0 380.0 600.0 100.0 240.0 380.0 600.0 100.0 240.0 380.0 600.0  w (mm) 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60  n 0.25 0.195 0.153 0.108 0.181 0.130 0.101 0.019 0.146 0.095 0.083 0.033 0.112 0.088 0.081 0.003 0.096 0.072 0.061 0.003  (MPa) 594.35 911.63 1004.5 1144.9 907.35 1156.8 1342.7 1188.3 1048.1 1245.4 1341.9 1272.9 1109.3 1268.9 1309.9 1199.8 1131.8 1149.7 1319.6 1261.6  IAB  TAB  T od  (°C) 186.05 242.55 274.58 323.37 270.13 309.31 351.55 330.12 292.29 321.12 354.65 352.45 300.07 331.53 353.61 340.25 308.48 302.42 352.76 351.16  (K) 259.25 4.39 263.94 2.97 268.31 2.76 279.83 2.62 316.26 3.56 309.02 2.56 317.33 2.39 295.30 2.37 333.29 2.99 321.11 2.34 327.56 2.33 314.94 2.31 340.86 2.68 333.10 2.32 334.07 2.26 315.12 2.28 349.37 2.57 321.02 2.27 337.22 2.24 324.16 2.20  m  IAB  (!/•) 118733.70 458321.87 803442.13 1368179.8 75792.602 283897.34 505902.38 812019.50 62882.582 220972.19 355570.53 568470.81 55045.316 168772.91 266665.50 436658.88 47182.918 141523.42 230122.25 379428.41  52  Chapter 3. Modeling of Machining with Sharp Tools  the effect of strain rate and cutting temperature on the flow stress (Ti  nter  at the tool-chip interface  zone. The velocity modified temperature in tool-chip interface zone T di t is given by mo  T  modint  where T ,  nter  + 273.0)(1 - ulog e  = {T  1Q  inter  )  inter  n  (3.56)  (K)  is temperature rise in secondary deformation zone at the tool-chip interface,  and v is material constant. For the steels, MacGregor and Fisher [20] found that v is about 0.09. Winter is strain rate in the secondary deformation zone. e j  n4er  is equal to jinter/VS as explained  before. Flow stresses (<TI and c r  intep  strain hardening index n, strain rate (JAB and jinter), and  ),  cutting temperature (TAB and Ti ) nter  are identified from machining test data as shown in tables  3.6 and 3.7. Flow stress exerted along the tool-chip interface is given by  (3.57) 6l w where Ff is mean friction force acting along the tool-chip interface. Ff is found by kinter =  7T, c  c  c  p F  fc  p • o k = R sinjj =  AB w sinB  1 A  B  (3.58)  s  cosu The empirical constitutive equations obtained from machining data will be used to determine flow stress associated with cutting process in the following sections. For the machining process, most of cutting energy is consumed in the primary shear deformation zone. The strain JAB and strain rate JAB are found to vary with the scale and speed of deformation defined by the undeformed chip thickness ti and cutting speed V (see the table 3.4). It is reasonably w  assumed that flow stress <TI is mainly affected by the strain and strain rate in the primary shear deformation zone. Therefore, empirical equations to establish the mapping of flow stress <TI  Chapter 3. Modeling of Machining with Sharp Tools  Table 3.7: F l o w stress o~i , cutting temperature T ; data nter  tl (mm) 0.02 0.02 0.02 0.02 0.04 0.04 0.04 0.04 0.06 0.06 0.06 0.06 0.08 0.08 0.08 0.08 0.10 0.10 0.10 0.10  v (m/min) 100.0 240.0 380.0 600.0 100.0 240.0 380.0 600.0 100.0 240.0 380.0 600.0 100.0 240.0 380.0 600.0 100.0 240.0 380.0 600.0  w (mm) 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3.60  Tinier  (!/•) 97003.532 602239.75 1168867.0 2146715.8 79053.859 462147.88 926871.06 1512345.8 81624.687 419976.19 686797.43 1111797.8 83395.046 326658.25 515050.09 874647.00 76591.242 287114.31 479449.68 825501.56  53  n t e r  Winter (MPa) 147.98 141.54 199.58 300.64 365.98 257.86 283.66 433.33 330.48 309.30 353.41 294.12 355.94 332.21 408.96 435.72 355.32 348.74 364.72 351.53  obtained from machining test  Tinter  ^modint  (°C)  (K) 297.56 305.24 342.52 419.04  246.62 335.92 447.54 654.88 466.98 543.37 682.01 1007.5 532.48 637.36 808.78 992.46 597.27 714.75 898.93 1257.1 644.67 725.04 932.14 1221.3  429.67 417.68 462.65 595.82 466.70 469.19 536.04 604.04 503.51 518.76 594.64 744.68 533.98 529.20 614.87 730.66  54  Chapter 3. ModeHng of Machining with Sharp Tools  and strain hardening index n from strain and strain rate in the primary shear zone are obtained as shown in Appendix B. Since temperature at the tool-chip interface is very high when cutting speed reaches certain value, strain hardening becomes insignificant in this zone. Oxley et al. [6], [36] also suggested that the strain hardening can be neglected due to very high strain existing at tool-chip interface. In this thesis, the mapping flow stress at the tool-chip interface (Ti  from the velocity modified  nter  temperature Tmodint is proposed, see Appendix B. Figure 3.13 (data from tables 3.6, 3.7) reveals the variations of experimental strain JAB, strain hardening index n, strain rate JAB, flow stress cxi, and temperature rise in the primary shear deformation zone TAB and the tool-chip interface zone T ;  n  t  e  r  with the cutting speed V  W  and undeformed chip thickness t in machining of P20 mold steel. x  From figure 3.13, the following features are observed • For the increase of cutting speed V , this involves a increase of deformation speed. W  Therefore, the strain rate is directly proportional to the cutting speed, so does the cutting temperature at the tool-chip interface. Temperature rise in the primary shear deformation zone show a slight increase due to the effect of adiabatic. Temperature rise in both primary shear and tool-chip secondary deformation zones causes strain softening. Strain hardening index n in the primary shear zone tends to decrease with the increase of cutting speed. • For the increase of undeformed chip thickness ti, this involves the increase deformation scale, flow stress is seen to increase. As a result, strain J B, strain rate JAB, and strain A  hardening index n decrease since the increase of temperature also leads to reduce strain hardening.  55  Chapter 3. Modeling of Machining with Sharp Tools  ti - undeformed chip thickness, o ti=0.02 mm, A ti=0.06 mm, 0 ti=0.10 mm  1  1500  A  £ 1000 ZA w  I  1  T~ - -  o  500  T  i i  0  i i i i_  u 1 400  200  1 600  CD  1 1 1 1 1  •a  J-  CO  A  Oj  | 0.1 c '« i= 0  1 800  i  1 1  -  ©- |  i i -  i i i  A -  200  —  400  Cutting speed V  i  i i  600  800  w  (m/min)  40  5  o  ^30 a>  c 4  o  c 2 3  +-* t/>  O)  A  0  -Or  Oi  600  I 1 U O  I I I  IIA:~~OT  :e == ! = = z p z : ==  10  H  200  400  600  800  Cutting speed V (m/min) w  O 1500  i  i i  !  - © — — x . —  1  - - -©A UI - — -  :6::ii:_-:L__  as CD  800  (m/min)  1  c 10° 'cfl  I I  w  1  I  i  i  i i  200  400  600  Cutting speed V (m/min)  1  400  1  200  Cutting speed V  10'  o  CD CO 10  1 1 . 1.1...1  CO  _Q_.  co  M i l M i l  o 2 .c  0  cc 20 _A_  L _  CO  j  i  ! I  rO-  Cutting speed V (m/min)  m <  i 1  0  fo.2  1 1  j  1  o  LL  1 1  ©  © j 1  1  I  — 1— 1  800  ti=)5.02  1 _--ti=(0.06  c o  TAB j 200  400  ti40.10  600  800  Cutting speed V (m/min) w  Figure 3.13: Flow stress, strain hardening index, shear strain, shear strain rate, and cutting temperature versus different cutting conditions  56  Chapter 3. Modeling of Machining with Sharp Tools  3.4  Prediction of Cutting Process with Sharp  Tools  Oxley et al. [36] initiated the analysis of machining process from work material properties and cutting conditions. Their theory accounts for the influence of cutting conditions on the flow stress, strain hardening, and strain rate. However, the determination of material properties under large plastic deformations are difficult to obtain from the standard material tests. Especially, high speed machining is characterized by very high strain rate and high temperature, which is hardly to evaluate from the conventional material tests. There are very few material test data under high strain rate and high temperature for P20 mold steel available in the literature. In this thesis, material constitutive relation for P20 work material is modeled through high speed orthogonal machining tests as demonstrated in the previous section. The Minimum Energy Principle is applied to predict shear angle for given cutting conditions and tool geometry through the model development. This section illustrates the procedures for the prediction of cutting process with sharp tools in detail.  3.4.1  A Minimum  Energy  Approach  The analysis of plastic deformations presented in the previous sections enables this model to obtain cutting energy associated with the machining process. The energy consumed in the primary shear and secondary deformation zones are superposed as the total cutting energy. Therefore, the prediction of shear angle is evaluated by comparing cutting energy from a set of trial shear angles. The true shear angle is found when cutting energy reaches the minimum. Figure 3.14 shows a generalized procedures of predicting shear angle 6, cutting energy E , c  cutting forces F and F , and cutting temperature rise in the primary shear deformation zone c  t  TAB and in tool-chip interface zone T j  n t e r  . As seen in figure 3.14, the input data consists  of undeformed chip thickness t\, width of cut w, cutting speed V , tool rake angle ct , and w  room temperature T . ROOM  0  Then, the outputs from this model are the predicted shear angle 6,  57  Chapter 3. Modeling of Machining with Sharp Tools  Stepl: Inputs t 1 , W, Vw, CCo, Troom  Step 2: Searching shear angle <|>1 < <|)i < <|)2 Strain and strain rate  ]  Step 3: Mapping flow stress a 1 and strain hardening index n from shear strain and shear strain rate. Mapping flow stress c inter from velocity modified temperature O 1, n, O inter  > Strain and stress relation CAB  =  Oi  6 AB  Step 4: Cutting energy E c = E s + E inter  E s Plastic power in primary shear zone E inter Plastic power in secondary deformation zone  Figure 3.14: A generalized cutting process evaluation algorithm for cutting with sharp edge tools  58  Chapter 3. Modeling of Machining with Sharp Tools  friction angle (3, cutting force F , feed force F , cutting energy per unit volume E , and cutting c  t  c  temperature rise in the primary shear zone TAB and cutting temperature rise at the tool-chip interface Ti . nter  The procedures for the prediction will be explained as follows.  In step 2, a trial shear angle fc for each iteration is selected first between fc and fc. fc and fc are scanned from 5° and 45°, respectively. Shear strain JAB and shear strain rate J B in A  the primary shear zone are calculated. Similarly, shear strain rate at tool-chip interface is also calculated. cosa  0  IAB  sinfccos(fc  JAB  Jinter  — >  (3.59)  cos(fc - Ct ) 0  sinfc t\cos(fc — a, sinfc  In step 3, flow stress <ri and strain hardening index n for the plastic deformation in primary shear zone are mapped from ^AB and JAB, which are evaluated using equations. 3.59 in step2. Then, flow stress <T B in the primary shear zone is evaluated by A  59  Chapter 3. Modeling of Machining with Sharp Tools  °~AB  k  A  B  IAB  CAB R  (3.60)  cos(6i + Qi — Ct )  A  0  A  &i - fc + Ct  F  k B  0  A  a  UB W  (1 -  TAB  X )F cosa s  s  0  pct\Wcos(fc — a ) a  T  inter  TB +  ^AT  A  M  k B t\w sinBi R sinQi sin<f>i cosOi Ff sin6 A  S  Ffc  c  AT,  pctiWcos(6 — a )  ^io(^)  0.06 - 0 . 1 9 5 ^ / ^ + 0.5Zo<7 (^)  T-rrxodirxt  AB.  s  10  'Tinier  Winter  where rj, tp, and \  (3.61)  0  (T  inter  + 273.0)(1 -  0.09^ e,„ r) l o  t e  are given in Appendix A . R is the resultant force acting on the slip-line S  0i and Bi are angle between resultant force and slip-line AB and friction angle at the  tool-chip interface corresponding to trial shear angle fc, respectively. Temperature rise for both in the primary shear zone TAB and in secondary deformation zone Ti  nteT  are calculated  as shown in figure 3.12. Once the velocity modified temperature T di t is obtained, the flow mo  n  stress ai ter exerted at tool-chip interface is identified from equations shown in Appendix B. n  60  Chapter 3. Modeling of Machining with Sharp Tools  In step 4, the total cutting energy is evaluated iteratively for each corresponding trial shear angle fc. Once the flow stresses <r\ and o-  inter  and strain hardening index n are identified for  the corresponding trial shear angle fc, superposing energy dissipation in the primary shear deformation zone E from Eqn. 3.35 and energy dissipation in the tool-chip interface zone s  Ei ter from Eqn. 3.39 yields the total cutting energy per unit volume (E ) n  c  E  _  <*\ y  j  COSCLQ  n  +  1  3<r  ^  n + l y/Z sinfc cos(fc — ct )  ;nter  l sinfc  ^  c  ^  4\/3 ti cos(fc — a )  0  0  where the contact length l is estimated from equation 3.45. The total cutting energy per c  unit volume E is compared iteratively for the different trial shear angles fc. Iteration continues c  until the E reaches the minimum. c  In step 5, the shear angle fc is predicted once the corresponding total cutting energy E  c  is found to be the minimum. Again, shear stress on the slip-line AB in the primary shear deformation zone (ICAB), friction angle 3, cutting temperatures T B and Ti A  nter  are predicted  as well when the identified shear angle fc is used in step 3. Therefore, cutting forces are predicted. Noted that the total predicted cutting forces F and F are obtained by summing up C  T  the forces contributed from the primary shear zone (F \ F ') and the edge forces generated by C  T  the flank-finish surface contact(F , F ) from equations C . l 1 in Appendix C. This approach is ce  TE  validated by Budak, Altintas, and Armarego [1].  61  Chapter 3. Modeling of Machining with Sharp Tools  6 - d> + a F cos(3 - a ) cos(d> + 3 - ct ) 0  a  Fj  a  0  a  FJ  0  (3.63)  F sin(8 — a ) COs((j) + 3 — 0L ) a  a  a  0  F' + F •i c i ce J  F' +F t  3.4.2  t<  M o d e l Verification  The model developed in this chapter aims to predict shear angle, mean friction angle on the tool rake face, cutting forces, temperature, strain rate in the primary shear and secondary deformation zones. This model mainly deals with machining with conventional sharp tools. Since machining removal rate is directly proportional to the undeformed chip thickness t\ and cutting speed V , it is of interest to evaluate cutting performance associated with various ti w  and V . The effect of undeformed chip thickness t and cutting speed V is analyzed by the w  x  w  proposed model in this chapter. The ranges of undeformed chip thickness ti : 0.02 ~ 0.11 m m and cutting speed V : 90 ~ 700 m/min are used in all model simulations. The experimental w  test ranges for t are 0.02, 0.04, 0.06, 0.08, 0.10 mm. The experimental test ranges for cutting x  speed V are 100, 240, 380, 600 m/min, respectively. Cutting tools used in experiments are all w  S A N D V I K S10 carbide tools with zero rake angle and 10° clearance angle.  Shear A n g l e d>  For the prediction of shear angle in machining process, first attempt was made to compare  62  Chapter 3. ModeUng of Machining with Sharp Tools  Cutting speed V (m/min) w  • A o  2 •  -  Merchant: < > | = TC/4 - [P - aJ/2 0.02  0.04 0.06 0.08 0.1 Undeformed chip thickness t (mm)  240 380 600 240 380 600  0.12  1  Cutting speed V (m/min)  0.02  0.04 0.06 0.08 0.1 Undeformed chip thickness t (mm)  0.12  1  Figure 3.15: Predicted shear angles by Merchant's [21]and Lee and Shaffer's [22] shear angle solutions  Chapter 3. ModeHng of Machining with Sharp Tools  63  the shear angles predicted by Merchant's [21] and Lee and Shaffer's [22] solutions with those evaluated from experiments. Figure 3.15 shows the prediction of shear angles applying the equations 2.9 and 2.11 proposed by Merchant and Lee and Shaffer. As Kobayashi et al. [24] pointed out, the agreement between the experimental shear angle and predicted results by their solution is poor. The predicted shear angles by Merchant's solution are close to experimental ones only when cutting speed V is very high with large undeformed chip thickness t\. The w  predicted shear angles by Lee and Shaffer's solution are close to experimentally evaluated shear angles as cutting speed is low. In figure 3.15, predicted shear angles by lines stand for the shear angle solutions obtained by Merchant [21] and Lee and Shaffer [22], respectively. Symbols represent the experimentally measured shear angles. Figure 3.16 shows the predicted shear angles by proposed model and shear angles obtained experimentally versus various undeformed chip thickness <i under three different cutting speeds, V , 240, 380, 600 m/min. The predicted results show good agreement with experimental rew  sults except when ti < 0.04mm. The predicted shear angles versus various cutting speeds are shown in figure 3.17. It can be seen that the predicted shear angles from the proposed model are better than that predicted by Merchant's and Lee and Shaffer's solutions as shown in figure 3.15 compared with experimentally measured shear angles . Both experimental and predicted shear angles show that shear angle changes insignificantly as undeformed chip thickness *i is larger than 0.05 mm and cutting speed V is higher than 240 m/min. w  F r i c t i o n Effects  As seen in figure 2.5, friction state affects the orientation of resultant force R exerted on s  the tool rake face. Friction state is observed to be varied with different cutting conditions. Figure 3.18 shows the variation of experimentally evaluated friction angles (equation 3.44) and measured contact length with various cutting speeds.  64  Chapter 3. Modeling of Machining with Sharp Tools  401  1  1  1  1  r  35 -  Undeformed chip thickness t (mm)  .14  Figure 3.16: Comparison of predicted shear angles by the proposed model with experimentally evaluated shear angles, w=3.6 mm, ct — 0°, V : 240, 380, 600 m/min. 0  w  65  Chapter 3. Modeling of Machining with Sharp Tools  45 •  •  Experimental - A  A  O  O  40 Predicted o  35  —  —  —  t =0.06 t =0.08 t =0.10 t =0.06 t =0.08 t =0.10 1  mrr mrr mrr mrr mrr mrr  -eO)  c  O  CO  -  *CD 30  A  x: CO  25  20 100  200  300 400 500 600 Cutting speed V (m/min)  700  800  w  Figure 3.17: Comparison of predicted shear angles by the proposed model with experimentally evaluated shear angles, w=3.6 mm, a„ = 0°, t\: 0.06, 0.08, 0.10 mm.  66  Chapter 3. Modeling of Machining with Sharp Tools  35  E  t = 0.04 mm 0.2  0  '  t  .0  0  A V  c?25 CO  c  +-* 0.15  t = 0.04 um  J 30  1  A  V;  v  O  0  § 20  c  o 0.1 O  D  200 400 600 Cutting speed V (m/min)  10  t = 0.08 mm  0  200 400 600 Cutting speed V (m/min) w  ^ = 0.08 mm  i  1  35  <  <  <  .. <  =£30  l» .9  2  200 400 600 Cutting speed V (m/min)  10 D  35 o  t = 0.10 mm  CO.  t  o  O) c CO  25 20  C  o  o  200 400 600 Cutting speed V (m/min)  o 15 LL 10 \  <  200 400 600 Cutting speed V (m/min) w  t =0.10 mm  30  tion  d)  o  0  •4—•  <1  <  ' 1  c  O  0 .  P  400 600 200 Cutting speed V (m/min) w  Figure 3.18: Variation of experimentally measured contact length l and friction angle 0 with cutting speed V . c  w  67  Chapter 3. Modeling of Machining with Sharp Tools  It can be seen that the variation of contact length l and friction angle 0 with cutting speed c  V shows a similar pattern. Both contact length l and friction angle 0 are relatively high when w  c  cutting speed is relatively low. l and 0 decrease with increasing of cutting speed. Again, c  further increase of cutting speed causes l and 0 to increase. This event indicates that contact c  length l is one of the most important factors which control friction states at the tool-chip c  interface. To explain this pattern, it is of interest to analyze the effects of shear flow stress kinter  along the tool-chip interface on the friction state. Since the resultant force (R ) acting a  on the slip-line AB in the primary shear zone is in equilibrium with the resultant force (R ') on a  the tool rake face.  R  a  k  B  A  h w  sinS cosO sin0  R' a  3 k i t e r lc  w  (3.64)  n  Asinj3 3 k i n t e r h sijl(j>  COs9  4k B t A  x  As shown in equation 3.64, the mean friction angle at the tool-chip interface 0 is proportional to the contact length l along the tool-chip interface. When the cutting speed increases c  up to certain value, the flow stress k i n t e r tends to decrease due to the effect of high temperature Tinter- Oxley et al. [6] also supported that the decrease of k j  n  t  e  r  is caused by the increase in  Tinter- The reason for the increase of friction angle at relatively high cutting speed may be attributed to the chipping of tool edge and fast tool wear.  Figure 3.19 shows the variation of predicted and experimentally calculated friction angles against cutting speeds. The variation of friction angles with cutting speed follows similar pattern aforementioned. But the deviation between the predicted values and experimental values is large. Possible reasons are the inaccurate prediction of resultant force angle 0 and shear angle  68  Chapter 3. Modeling of Machining with Sharp Tools  45  40-  •  •  t =0.06 mrr  Experimental - A  A  t =0.08 mm  O  O  t =0.1 mm  1  1  1  t =0.06 mnr 1  35  Predicted  t =0.08 mrr —  o  —  —  t =0.1 mm 1  co.  -£30 C CO  c o T3 25 20  s 15  10  100  200  300  400  500  600  700  800  900  Cutting speed V (m/min) w  Figure 3.19: Predicted and experimentally determined friction angles versus various cutting speeds, w=3.6 mm, ct = 0°, t i : 0.06, 0.08, 0.10 mm. 0  69  Chapter 3. Modeling of Machining with Sharp Tools  6, which are used to predict friction angle from equation 3.63.  Figure 3.20 shows the predicted and experimental friction angles against various undeformed chip thickness. The predicted results show good agreement with those obtained experimentally at cutting speed V = 600 m/min. From experimental values, it seems that friction angle show W  little variation with undeformed chip thickness. Again, the deviation between experimentally evaluated friction angles and predicted is possibly due to the inaccurate measurement of contact length along the tool rake face.  Cutting Energy E  c  In machining process, the efficiency of the machining under certain cutting conditions can be evaluated by using the cutting energy per unit volume E (J/rom ). The predicted cutting 3  c  energy from the proposed model is determined from equation 3.62. The cutting energy per unit volume E is evaluated from experiments by c  ce  E = c  (3.65)  The variation of predicted and experimentally determined cutting energy per unit volume of cut with cutting speed is shown in figure 3.21. The predicted cutting energy E shows good c  agreement with experimental cutting energy. It seems that the cutting energy E shows the same c  trend as the variation of contact length l and friction angle 3 with cutting speed. Cutting energy c  per unit volume tends to be higher when cutting speed is relatively low and high. The results from tool wear tests suggest that the tool wear in terms of flank wear VB is relatively low at the cutting speed of 240 m/min among a range of cutting speeds V : 60,120,240,380,600m/ram W  (*i=0.06 mm).  Chapter 3. Modeling of Machining with Sharp Tools  70  Figure 3.20: Predicted and experimentally determined friction angles versus various undeformed chip thickness, w=3.6 mm, a„ = 0°, V : 240, 380, 600 m/min. w  Chapter 3. Modeling of Machining with Sharp Tools  2.7-  Experimental -  71  •  •  A  A  O  O  t =0.06 mrr t =0.08 mrr t =0.1 mm t =0.06 mrr t =0.08 mrr t =0.1 mm 1  1  1  1  Predicted -  1  —  100  200  —  —  300 400 500 600 Cutting speed V (m/min)  1  700  800  w  Figure 3.21: Predicted and experimentally determined cutting energy per unit volume of cut, w=3.6 m m , a = 0°, t \ 0.06, 0.08, 0.10 m m . 0  x  72  Chapter 3. Modeling of Machining with Sharp Tools  Cutting speed V (m/min)  •  •  A  A  O  O  2.6 Experimental -  2.4  Predicted -  E E  —  o  -2.2  o  CD CD  ~A~ -  —  —  240 380 600 240 380 600  O -  " ~ ~ - - -A-  CD  A  c 3  o  1.8  1.6  1.4  0.02  0.04  0.06 0.08 0.1 Undeformed chip thickness t (mm)  0.12  0.14  1  Figure 3.22: Predicted and experimentally determined cutting energy per unit volume of cut, w=3.6 mm, a = 0°, V : 240, 380, 600 m/min. 0  w  73  Chapter 3. Modeling of Machining with Sharp Tools  Figure 3.22 shows the variation of predicted and experimentally determined cutting energy per unit volume of cut with undeformed chip thickness t\. The predicted results are close to the experimental results.  C u t t i n g T e m p e r a t u r e s TAB a n d T ;  nter  The energy consumed in cutting process is largely converted into heat in the primary shear deformation and the tool-chip interface zones. In fact, tool wear is mainly attributed to the high compressive stress and high temperature exerted on the cutting tool. Trent [45] suggested that tool wear of carbide tools show less sensitivity to the cutting temperature rise at the tool-chip interface up to 1200° C. Cutting temperature rise in the primary shear zone TAB is predicted from equation 3.60. Temperature at the tool-chip interface T  inter  The predicted cutting temperatures TAB and Ti  nter  from equation 3.61.  against cutting speed is shown in figure  3.23. The cutting temperature TAB in the primary shear zone shows the less dependency on the changes of cutting speeds. For a range of cutting speeds (100 ~ 600m/mm), the variation of TAB is about 300 C ~ 400 C. Oxley and Stevenson [62] explained that TAB 0  0  rises rapidly at low cutting speed V due to rapidly changing the ratio A, (see in Appendix w  A). The temperature rise tends to be adiabatic with little heat conducted into the work material when cutting speed is higher. Therefore, T B remains approximately constant. The strain rate A  increases approximately linearly with cutting speed and strain hardening decreases with the increase of cutting speed as seen in figure 3.13. Cutting temperature TAB reaches adiabatic state as result of high cutting speed. For the temperature rise at tool-chip interface Ti , it can nter  be seen that T ;  nter  is almost proportional to the cutting speed. It is apparent that the friction is  much more severe along the tool-chip interface when cutting speed gets higher. Figure 3.24 show the variation of predicted cutting temperatures TAB and Ti  nter  with  undeformed chip thickness ti. Since heat generated in the primary shear deformation zone  74  Chapter 3. Modeling of Machining with Sharp Tools  O 450 m  -i  1  1  r  Predicted temperature rise in the primary shear zone  Z3»  §350 Q.  ^=0.06 mrr ^=0.08 mrr ^=0.1 mm  E ~ 300 CD  c  O 250  100  200  300  400 500 600 700 800 Cutting speed V (m/min)  900  1000 1100  w  O  ,2000 -  Predicted temperature rise at the tool-chip interface  §1500 CD  ^=0.06 mrr ^=0.08 mrr ^=0.1 mm  E1000 0) CO  3  O  500 100  200  300  400 500 600 700 800 Cutting speed V (m/min)  900  1000 1100  w  Figure 3.23: Predicted cutting temperatures rise in the primary shear zone and the tool-chip interface zone versus cutting speed, w=3.6 mm, a = 0°, t : 0.06, 0.08, 0.10 mm. 0  x  75  Chapter 3. Modeling of Machining with Sharp Tools  0 500 o  Predicted temperature rise in the primary shear zone Cutting speed  S 400 CO  V  g_350 £ S 300  1 250 3  0.02  O ~£ooo c  0.04  0.06 0.08 0.1 0.12 Undeformed chip thickness t (mm)  240 380 600 0.14  Predicted temperature rise at the tool-chip interface  I—~ 3 CO  (m/min)  —— —  CO  o  w  Cutting speed  1500  V  w  (m/min)  \  e 1000 CD —  CO  c  o  500  0.02  0.04  —  0.06 0.08 0.1 0.12 Undeformed chip thickness t (mm)  —  240 380 600 0.14  Figure 3.24: Predicted cutting temperatures rise in the primary shear zone and the tool-chip interface zone versus undeformed chip thickness t i , w=3.6 mm, a = 0°, V : 240, 380, 600 m/min. Q  w  Chapter 3. Modeling of Machining with Sharp Tools  76  is proportional to the strain energy E , predicted temperature rise in the primary shear zone s  shows less variation with the undeformed chip thickness. The temperature rise at the tool-chip interface T  inter  increases slowly with the increase of ti at low cutting speeds. However, T ;  nter  changes rapidly with the increase of undeformed chip thickness 11 at high cutting speed. The comparison between tool wear rate observed from experiments and corresponding predicted cutting temperature in the primary shear and secondary deformation zones under a range of cutting speed is shown in figure 3.25. It can seen that cutting tool gets worn rapidly once cutting speed is higher than 240 m/min. Predicted cutting temperature at the tool-chip interface indicates that temperature reaches diffusion point of Cobalt binding material used S10 carbide tools when cutting speed increase beyond 240 m/min. It is found that cutting speed V =240 m/min, corresponds to the minimum wear rate. S E M analysis indicated that adhesion w  is dominant under the cutting speed lower than V =240 m/min and diffusion is active above the w  cutting speed K,=240 m/min.  C u t t i n g Force F a n d F c  t  The surface finish, cutting temperatures, and tool life are directly influenced by the cutting forces. The variation of predicted cutting forces (F , F ) with cutting speed and undeformed c  t  chip thickness are compared with those measured from experiments. The predicted cutting force F and feed force F are found from equation 3.61. Figure 3.26 c  t  show the predicted and experimentally measured cutting forces versus various cutting speed. The equation 3.61 indicates that the decrease of cutting forces F and F are due to the increase c  t  of shear angle as the cutting speed is changed from 90 to 240 m/min. Further increase of cutting speed V does not lead to significant reduction of cutting forces. Predicted results show close w  agreement with experimentally measured forces. Figure 3.27 shows the variation of predicted and experimentally measured cutting forces  77  Chapter 3. Modeling of Machining with Sharp Tools  t = 0.06 mm, w=5.0 mm  in primary shear zone in tool-chip interface zone  <o 1500 CD  2.1000 t3 500 100  200  300 400 Cutting speed V (m/min)  500  600  700  w  x 10 o  o  Experimental wear rate measurement  t. = 0.06 mm, w=5.0 mm o  £4  & 2 3 CO CD 2  o o  o  100  200  300 400 Cutting speed V (m/min)  500  600  700  w  Figure 3.25: Plot of predicted cutting temperatures TAB and T j and experimentally measured wear rate versus cutting speed, w=5.0 mm, a = 0°, t\\ 0.06 mm. n t e r  Q  78  Chapter 3. Modehng of Machining with Sharp Tools  Line: Predicted, Symbol: Experimental  • A O  200  800 400 600 Cutting speed V (m/min)  t =0.06 mrr =0.08 mrr =0.1 mm =0.06 mrr =0.08 mrr =0.1 mm 1000  1200  1000 •  800  A CD O  600  "D  400  CD CD  O  200 200  800 400 600 Cutting speed V (m/min)  t =0.06 mrr t =0.08 mrr t =0.1 mm t =0.06 mrr t =0.08 mrr t =0.1 mm 1000  1200  Figure 3.26: Predicted and experimental measured cutting forces versus cutting speed, w=3.6 mm, a = 0°, h: 0.06, 0.08, 0.10 mm. 0  79  Chapter 3. Modeling of Machining with Sharp Tools  V =240 m/min w  V =380 m/min w  V =600 m/min w  V =240 m/min w  V =380 m/min w  0.02  0.04  0.06 0.08 0.1 0.12 0.14 Undeformed chip thickness t (mm)  V =600 m/min w 0.16 0.18  1  •  V =240 m/min  A  V =380 m/min  O  V =600 m/min  w w w  V =240 m/min w  100  0.02  0.04  0.06 0.08 0.1 0.12 0.14 Undeformed chip thickness t (mm)  V =380 m/min w Vw=600 m/min 0.16 0.18  1  Figure 3.27: Predicted and experimentally measured cutting forces versus undeformed chip thickness ti, w=3.6 mm, ct = 0°, V : 240, 380, 600 m/min. 0  w  80  Chapter 3. Modeling of Machining with Sharp Tools  against undeformed chip thickness t . The cutting force component F is close to experimental x  c  cutting force component. There exists some deviation especially for the feed force component F . Possible errors may come from inaccurate analytical prediction of friction angle 0 from t  equations 3.61.  Shear stress i n the p r i m a r y shear zone  Figure 3.28 shows the predicted and experimentally calculated shear stresses versus cutting speed.  The experimental shear stress is evaluated from the measured cutting forces and  experimental shear angle using the equation 3.46. The predicted shear stress is found from the equation 3.60 when shear angle is predicted from given cutting conditions. The predicted shear stress shows close agreement with that evaluated from experiments except at cutting speed V  w  < 150 m/min. The comparison between the predicted shear stress and experimental shear  stress against undeformed chip thickness is show in figure 3.28. The predicted shear stress also shows close agreement with experimentally evaluated shear stress. One can note that the accurate prediction of shear stress is needed in order to predict cutting forces accurately.  3.5  Summary A model for high speed orthogonal machining with conventional sharp tools is presented  in this chapter. The proposed model involves establishing P20 material constitutive relation under high strain rate and high temperature through orthogonal machining test and analyzing plastic deformation in the primary shear and the tool-chip interface zones. Strain, strain rate, stress, and temperature are evaluated using the model proposed by Oxley et al. [6], [36]. The energy dissipation in the primary shear and the tool-chip interface zones are formulated. The Minimum Energy Principle is applied to predict shear angle in machining process. By  81  Chapter 3. Modeling of Machining with Sharp Tools  900  850 CO Q_  Uncut chip thickness Experimental 600  •  •  A  A  O  O  Predicted —  550  100  200  300  --  —  400 500 600 700 cutting speed V (m/min)  0.06 mm 0.08 mm 0.1 mm 0.06 mm 0.08 mm 0.1 mm  800  900  1000  w  Figure 3.28: Predicted and experimentally evaluated shear stress in the primary shear zone versus cutting speed, w=3.6 mm, a = 0°, t\\ 0.06, 0.08, 0.10 mm. 0  82  Chapter 3. Modeling of Machining with Sharp Tools  Figure 3.29: Predicted and experimentally evaluated shear stress in the primary shear zone versus undeformed chip thickness t-i, w=3.6 mm, a = 0°, 14,: 240, 380, 600 m/min. 0  Chapter 3. Modeling of Machining with Sharp Tools  83  inputting the undeformed chip thickness, cutting speed, width of cut, main rake angle, and room temperature, this model enables process planer to estimate forces and temperature for cutting P20 mold steel under a different cutting conditions.  Chapter 4  Modeling of Machining with Chamfered Tools  4.1  Introduction In practice, machining process is optimized based on some variables, such as the tool wear  rate , cutting temperature, cutting forces or power, chatter, surface finish, and dimensional errors left on the workpiece. The quest for low costs and high productivity has led to the high speed machining and intelligent machining process control. High speed machining means high material removal rate. In the high speed machining of dies and molds, tool wear is one of the major concerns. The performance of a cutting tool, or the machinability, is measured in terms of tool life, surface finish, and metal removal rate as a function of tool geometry, feed and cutting speed, and work material properties. The machinability study is usually carried out by conducting series of cutting tests and tool life measurements in industry. Tool geometry plays an important part in the cutting performance. In general, negative rake geometry enables the brittle cutting tool to sustain heavy cutting and strengthens the edge of cutting tool. However, negative rake geometry leads to larger cutting forces than positive rake, and consequently results in higher temperatures. High positive rake angle has the advantage of reducing cutting forces at the expense of weakening cutting edge of the tool. Since the tool starts wearing from the cutting edge, optimizing the edge geometry is also an avenue to improve cutting performance. Unfortunately, conventional tool geometry design is often carried out by trial and error methods. The aim of fundamental research in cutting mechanics is to minimize the number of costly machining tests, and narrow the optimal tool geometry design and cutting conditions by  84  Chapter 4. Modeling of Machining with Chamfered Tools  85  predicting them analytically. Such an attempt is made in high speed machining of hardened P20 mold steels with chamfered carbide and C B N tools in this chapter. There are three basic ways in which the cutting edge is usually prepared: honed radius on the actual corner, a chamfer which breaks the corner, and land, stretching back negatively from the clearance side to various lengths on to the insert face [63]. In modern machining practice, cutting inserts with designed chamfered cutting edge are commonly introduced by cutting tool industry to enhance the cutting tool performance under certain circumstances. The investigations of cutting with chamfered edge tools have been carried out by some researchers [39], [46], [47], [3], [50]. However, a comprehensive understanding about the insight into the machining with chamfered tools is still not available. In this chapter, a comprehensive analytic model of the process is developed. The plastic deformation is separated into the primary shear, dead metal zone created by the chamfer, and the secondary deformation zone where the chip moves over the regular rake face of the tool. Oxley's [6] slip-line field with strain, strain rate and temperature dependent flow stress model is extended to model primary and secondary deformation zones. The flow stress of the material is calibrated as a function of strain, strain rate and temperature from orthogonal machining tests with sharp tools, as opposed to high-speed compression tests. The dead metal zone is modeled as an extrusion process, where the dead metal boundary is assumed to act like the wall of a die. The total contact length between the chip and the regular face of the cutting tool rake was expressed as an empirical function of uncut chip thickness, and calibrated from experimental observations. The sticking and sliding chip contact lengths are considered to be equal in modeling the total friction force on the rake. The shear angle is estimated by minimizing the energy consumed in the three deformation zones. The proposed model predicts the shear angle, cutting forces, and cutting temperature from given cutting conditions. The proposed model is verified with high speed orthogonal cutting tests using both ISO S10 carbide and C B N tools applied on P20 mold steel work material. It is shown that the proposed model is able to identify the most  86  Chapter 4. Modeling of Machining with Chamfered Tools  optimal chamfer angle and cutting speed, which yields lowest tool wear and relatively lower cutting forces.  4.2  Modeling of Plastic Deformation for Cutting with Chamfered Tools In high speed machining with chamfered tools, plastic deformation under the chamfered  edge must be taken into account since a chamfered tool has different mechanics than a sharp edge tool concerning the chip formation as presented in chapter 3. To analyze the chip formation for such tools, a cutting mechanics model is proposed as shown in figure 4.1. The proposed model assumes that a surface layer of work material defined by the undeformed chip thickness i i flows into the primary shear deformation zone, and separates at a stagnant point B, see figure 4.1. The velocities of workpiece, shear and chip are indicated as V , V„, and V , respectively. w  c  From point B, some of the material is trapped in the dead zone created by the chamfer, where the material flows over towards the regular rake face and forms the chip. Chamfer geometry is defined by the length of chamfer edge (b f) and chamfer angle (second rake angle c*i). The c  proposed slip line field is used to form energy equations for primary shear zone (AB), chamfered zone (OH) and secondary deformation zone where the chip flows over the regular rake face (HG). The energy equations are used to predict the shear angle, force and temperature while considering the flow stress, strain, strain rate and temperature effects. Again, plane strain, steady-state continuous chip formation are assumed in this model. Following the similar approach presented in chapter 3, the analysis of strain, strain rate, temperature, and energy dissipation in the primary shear, dead metal and secondary deformation zones is carried out as follows.  Chapter 4. Modeling of Machining with Chamfered Tools  Figure 4.1: A proposed chip formation model for cutting with chamfered tools  Chapter 4. Modeling of Machining with Chamfered Tools  4.2.1  88  Plastic Deformation in the Primary Shear Zone  The same method to determine strain and strain rate presented in chapter 3 is applied here. Slip-line AB in the primary shear zone is assumed to be the line of maximum shear strain and shear strain rate as proposed by Oxley et al. [6], [36], seefigure4.1. Shear strain JAB and shear strain rate JAB in the primary shear deformation zone are given by the following equations COSOL  0  lAB  =  sinfc cos(fc — a ) 0  lAB  =  V,  =  V„  IAB  At  =  V  W  1  A  (4.1)  TA~B  B  COSCio  cos(fc - a ) 0  IAB  1 ) •'AB  h  sinfc  where a„, fc, IAB, V are main rake angle of cutting tool, shear angle, length of shear line AB, 3  and shear velocity along AB. S is taken to be about 6.0 as explained in chapter 3. C  From Von-Mises yield criterion, shear flow stress ( k A B ) distributed along A B in the primary shear zone is found by GAB  =  £AB  =  k B A  =  O-IEAB lAB  V3 CAB  VZ ~  C\  v/3  k A B IAB W  where  crAB,  (4.2)  tAB  &\ £AB  V3  AB W  n, and F are flow stress, strain hardening index, and shear force along the slip-line a  AB, respectively. <TI and n are found by evaluating the shear stress, shear strain and strain rate (equations 4.1) from a set of orthogonal cutting tests, see equations B.5 in Appendix B. As proposed by Oxley et al. [6], [36] and Boothroyd [19], the temperature rise in the primary shear zone is predicted by  (4.3)  Chapter 4. Modeling of Machining with Chamfered Tools  89  The procedure to calculate temperature in the primary shear zone is shown in the Appendix A. Again, the energy dissipation in the primary shear deformation zone is determined as expressed by  <T\  cosct  n+l  0  (4.4)  n + l y/^ sinfc cos(fc  4.2.2  Plastic Deformation in the Chamfered Edge Zone  This section explains the modeling of plastic deformation due to the chamfer based on the analysis of strain, strain rate, temperature converted by the plastic work, and energy dissipation in chamfered edge zone. Figure 4.2 illustrates a postulated slip-line field for cutting with chamfered tools. The primary shear deformation zone (AB) is connected to the slip-line field in the chamfered edge zone by a central fan BCI, see figure 4.2. Similar to extrusion process, the initial undeformed work geometry before entering the chamfered edge zone (h ) plastically deforms and leaves 0  the edge with a thickness of hf. It is assumed that the dead metal trapped in the chamfered zone forms a slope identical to the primary shear angle, i.e. fcf = <f> . Slip-line EF meets s  free boundary surface at —. The velocity field corresponding to a slip-line field can represented by a hodograph. If a valid hodograph, which satisfies the velocity boundary conditions, can be constructed for a field with the non-negative rate of energy dissipation throughout the field, the slip-line field is kinematically admissible [26]. The analysis of slip-line field is based on  Chapter 4. Modeling of Machining with Chamfered Tools  90  a deformation field that is geometrically consistent with the shape change. Furthermore, the stress within the field are statically admissible. The proposed model mainly focuses on the analysis of energy consumption in two aspects, which consist of the strain energy in the chamfered zone and the frictional energy along the dead metal interface.  From geometrical relation of slip-line field in the chamfered edge zone, the mean plastic strain and strain rate are formulated as b f sinoci b f sinoci (1 + tanSg) tan<f> c  = 1  c  3  1 + tan<f>  1 + tancj>  a  hf  s  (4.5)  b f sinai c  b f sinai(l + tan6 ) e f V tan6 e fV c  B  c  w  s  c  b f sinai tan<j> c  w  b f sinai  s  c  The energy dissipated in the chamfered edge zone is contributed by the plastic work (Ei) in extruding the material from thickness h to hf and the friction energy (Ef) consumed at the 0  dead metal interface (BO). Similar to extrusion process, the " Dead Metal Zone " under the chamfered edge during cutting acts as a die. The plastic energy per unit volume consumed in the chamfered edge zone Ei is  Ei = <J f e f c  c  (4.6)  where <r f is flow stress which varies with strain, strain rate, and temperature rise in the c  chamfered edge zone, see equations B.6 in Appendix B.  Chapter 4. Modeling of Machining with Chamfered Tools  Figure 4.2: A proposed slip-line field for cutting with chamfered tools  91  92  Chapter 4. Modeling of Machining with Chamfered Tools  Similar to extrusion process, the " Dead Metal Zone " under the chamfered edge during cutting acts as a die. BO is the boundary to separate deforming work material and die surface. The energy per unit volume Ef by friction work done at interface BO is mainly affected by the product of friction force FBO and shearing velocity VBO along the interface BO. BO  bcf  T  FBO V  BO  =  sinai  w  *  COS(f>  s  v  w  =  cosd>  (4.7)  s  cos2d> k f  1~BO =  kf  -  c  where r o and k B  cf  s  c  V3  is shear stress exerted along interface BO and shear flow stress along  slip-line CO in the chamfered edge zone, respectively. r o is found from Mohr circle as shown B  in 4.2. The energy per unit volume Ef by friction work done at interface BO is formulated by FBO VBO  V hw w  0  TBO b fsincti w VBO V h w cos<f> c  w  0  s  (4.8) cos2d> k s  cf  cos d> (1 + tand> ) 2  a  s  cos2d> o~ f s  y/Zcos d> (l 2  s  c  + tand> ) s  Hence, the total energy consumed in the chamfered edge zone E f is determined by superposing c  strain energy Ei and friction energy Ef.  Ef c  = Ei + Ef  93  Chapter 4. Modeling of Machining with Chamfered Tools  e  <T c i  +  Q-cfCos26  a  \/3 cos 6 (l + tan6 )  c f  2  s  s  Heat generated by the plastic energy E f causes temperature rise in the chamfered zone. c  Temperature rise in the chamfered zone T f is given by c  T  ef  4.2.3  =T  (4.10)  + ^pc E  A B  Plastic Deformation in the Tool-Chip Interface Zone  In the modeling of machining with chamfered tools, the evaluation of strain rate, temperature, and energy dissipation in the secondary deformation zone is carried out using the same approach as presented in chapter 3. The strain rate (jinter) at the tool-chip interface is approximated by Oxley et al. [6], [36] as  Kinter  —  V_ 8 • t V .. .<tir>./h. sin6„ cos(6 - a ) t\ cos(6 — a ) sin<j>g 2  w  s  (4.11)  0  s  0  where V and t are the rigid chip velocity and the chip thickness, respectively. S is the ratio c  2  of thickness of plastic deformation zone at the tool-chip interface to the chip thickness t . 8 is 2  taken to be 0.05 as explained in chapter 3. Both thermal and energy analysis in tool-chip interface zone require the tool-chip contact length l as a known parameter. Gad and Armarego et al. [35] reviewed several approaches c  to determine tool-chip contact length in the literature. They concluded that the most adequate method of contact length estimation is to use empirical equations obtained from measurements  94  Chapter 4. Modeling of Machining with Chamfered Tools  in machining tests. In this model, the following relationship is assumed between the contact length (7 ) and uncut chip thickness (ti) C  Z = m-i ix  (4.12)  c  where m i is an empirical constant evaluated from orthogonal machining tests on P20 mold steel, m i is found to be about 3.20 for S10 carbide tools and 1.3 for MB820 C B N tools, respectively.  The temperature rise (Tinter)  at the tool-chip interface for chamfered tools is given by  T  inter  = T  + i > A T  cf  M  (°C)  (4.13)  where T f is temperature in the chamfered zone. The determination of A TM is explained c  in Appendix A . Once temperature at the tool-chip interface T ; temperature T n moi  nt  nter  is evaluated. The velocity modified  at the tool-chip interface is evaluated by T  modint  = (T  i n t e r  + 273.0)(1 - Omog (^)) 10  (4.14)  Then, the flow stress at tool-chip interface is mapped from velocity modified temperature Tmodinter  as shown in Appendix B.  As flow stress f 7  i n t e r  and contact length l are identified, the energy per unit volume dissipated  in tool-chip interface zone E i  c  n  t  e  r  is found by Ft V  Jointer  V tiW w  (4.15)  4V Uw 3 (Ti ter 'c sin6{ w  n  4ti cos(<f>i — a ) , 0  95  Chapter 4. Modeling of Machining with Chamfered Tools  4.2.4  P r e d i c t i o n of C u t t i n g Process with C h a m f e r e d T o o l  Similar to the model development in chapter 3, the inputs here are cutting conditions, tool geometrical parameters (including chamfer geometry), and work material mechanical properties. The outputs are the predicted shear angle, cutting forces, strain and strain rate, and temperature in the primary shear and the tool-chip interface zones. The total cutting energy per unit volume E is obtained by summing up the energy dissipated c  in the three plastic deformation zones (equations 4.4,4.9,4.15).  p  °"1 r o ln+1 , „ n + 1 V3 sind> cos(<f> — a ) COSOC  L  a  a  0  c  ,  (T cos2<f> y/3 cos d> (\ + tan<j> ) cf  s  2  s  s  Zo-jnter h sitl<f>  a  4 ^ 3 ti cos(<f> — a ) a  0  The total energy is dependent on the shear angle, tool-chip contact length, flow stress in each plastic work zone, rake angle and chamfer geometry. However, the flow stress in each zone is also dependent on the local shear strain, strain rate and temperature, which are in turn dependent on the shear angle. It is proposed that applying the minimum energy principle can solve such a complex deformation process. The iterative solution procedure is summarized in figure 4.3, where the input data contains cutting speed, width of cut, uncut chip load, tool-chip contact length and tool geometry. The iteration starts with an initial guess value of shear angle. The corresponding temperature, shear strain, strain rate and flow stresses in the three plastic zones are evaluated from orthogonal cutting database. The flow stress of the material is modified as a function of temperature, strain and strain rate as explained before. The total cutting energy is then evaluated from Eqn. 4.16. The iteration is repeated by scanning the realistic shear angle range (d>i = 5°  96  Chapter 4. Modeling of Machining with Chamfered Tools  Step 1: Inputs  V , t], W, 0C , OCi, brf, X ^ n , I,. w  o  Step 3: Mapping S t r a i n £AB>£<f  •  •  S t r a i n rate ^ B » £ c f , Stresses ° A B >  • Winter  ? ^mta-  t Step 4: C u t t i n g energy  E ^E E + E C  S+  cf  •  inter  E * P l a s t i c p o w e r i n the p r i m a r y shear zone E c f P l a s t i c p o w e r i n the c h a m f e r e d edge zone £ inter P l a s t i c p o w e r i n tool-chip interface zone  No  Yes  ' Step 5 : O u t p u t s S h e a r angle, f r i c t i o n angle C u t t i n g energy; cutting forces C u t t i n g temperatures  Figure 4.3: A generalized prediction algorithm for cutting with chamfered tools  97  Chapter 4. Modeling of Machining with Chamfered Tools  to d> = 45° ), and the shear angle which corresponds to the minimum energy is accepted as 2  a solution. The minimum energy principle was first applied by Merchant [21] for orthogonal cutting without strain and thermal affects. Shamato and Altintas [2] applied the same principle to oblique cutting, again without strain and thermal affects. However, they used shear stress and friction coefficients evaluated from orthogonal cutting tests, which improved the prediction accuracy significantly. The past studies considered only cutting with sharp edge tools. Unfortunately, the same approaches can not be applied due to the chamfer. Furthermore, the aim of the work is to predict the behavior of cutting process at high cutting speed range where the thermal softening and strain - strain rate dependent flow stress play an important role, which are considered in the proposed model. Similar to the analysis of temperature for a sharp tool model presented in chapter 3. An iterative procedure is applied to evaluate temperature in three characterized plastic deformation zones as illustrated in figure 4.4. For each selected trial shear angle d>i, the inputs to calculate cutting temperature in three zones consist of undeformed chip thickness t , tool main rake angle a , width of w, room 0  x  temperature T , ROOM  shear force F , friction force Ff , and energy consumption in the chamfered a  c  edge zone E f, respectively. Thermal conductivity («) and specific heat (c) as a function of c  corresponding temperature evaluated in each plastic deformation zone are given in Appendix A . The empirical factor, the proportion of heat conducted into work material (A,), is given in Appendix A. The initial temperature of work material or room temperature is assigned to calculate the temperature in the primary shear zone as proposed by Boothroyd [19] and Oxley et al. [6], [36]. The temperature at the tool-chip interface is expressed approximately by summing up the temperature rise in the chamfered zone T f and maximum temperature rise in the chip c  material on passing along the tool rake face ATM•  98  Chapter 4. Modeling of Machining with Chamfered Tools  Inputs: 11, ao, W, Troom, Fs, Ffc, Ecf, <|)i, Is, T|, \|/  7  Initialize: T.„ = T.  Temperature rise in primary shear zone K = 28.74 + 0.0053 T ; pc = 3.59 x 10 - 100.0 T ; [ ( l - X , ) F , cosa ] PC, K , X . , F E X > . - = r . o [ p c t, w CO 6  AB  AB  0  T  T  s  m  Temperature rise under the chamfer zone pc = 3.59 x IO - 100.0 T 6  cf  pc, E  cr  EZ>  T,= T  AB  +  ^pc  No  Initialize: T  lnt(!r  =T  cf  Temperature rise in tool-chip interface zone K = 28.74 + 0.0053 T ; pc = 3.59 x 10 - 100.0 T 6  lnur  F , K , pc, AT [C  No  |  y  T i n t t r  =  Trf  +  v  A  T  lnt<r  ;  m  Yes -•Output T  lnlt  Figure 4.4: A procedure to estimate cutting temperatures for cutting with chamfered tools.  99  Chapter 4. Modeling of Machining with Chamfered Tools  Once the shear angle is identified, the friction angle at tool-chip interface is predicted by 3  =  8 - <j>,  + <x  0  (4.17) tan0  =  [1 + 2(f - 4>,)] -  Sn c  where 8 defines the inclination between the resultant force vector R and slip-line AB (see Fig. s  4.1). S is taken as S ca 6.0. The total tangential (F ) and feed (F ) cutting forces are in the c  c  c  t  direction of cutting velocity V and perpendicular to it. They are obtained by resolving the forces w  contributed from primary shear zone (FJ, F '), chamfered zone ( F _ / , F _ / ) and edge forces c  t  c  t  c  generated by the flank-finish surface contact ( F , F/ ) in the two directions aforementioned. ce  F  c  F  t  e  =  F' + F - f  =  F / + Ft-cf + Fu  c  c C  + F  c e  (4.18) ,  The cutting forces generated in each deformation zone are evaluated as follows.  The  edge forces are identified from machining tests by extrapolating the cutting forces at zero chip thickness (Budak, Altintas, and Armarego,[l]). The shear force on shear plane (AB) is evaluated from equations 4.2, which leads to resultant force R  s  = FJ  cos9. Note that the  resultant force (R ) does not contain the forces contributed by the chamfered zone, but it is s  counterbalanced by the forces acting on the regular part of the tool rake face (HG), see figure 4.1. The contributions of primary shear zone to tangential and feed forces ( F ' , F / ) are given c  from the geometrical relations  FJ  =  F,cos(0 - a )  )  0  COs(<j) + 3 - Ct ) 0  s  (4.19) FJ  F sin(3 - a ) cos(d> + 3 - a ) 3  0  s  0  ,  100  Chapter 4. Modeling of Machining with Chamfered Tools  The force components F - f  and F - f  c C  generated at the chamfered zone are evaluated  t C  from the normal and tangential stresses distributed along the dead metal interface BO. Using Hencky's equations (Johnson et al. [26]) with Mohr circle shown in figure 4.2  CTEF  =  o-co  =  CTBO  = - {o~co + k sin2fc)  TBO  =  —  -Kf(l  along EF + -i)  along EC  3  along BO  cf  cos 2fc k f  along BO  c  The corresponding forces in chamfered zone are Fc-cf n  F -cf t  = =  [(TBocosds + O-BO sinfc) u  [{O-BO  j  cosq> • i \°cfsinaiw sinfc) 7 cos<p  (4.21)  s  cosfc - T  bo  J  s  Where b f, a c  u  and w are the length of chamfer, chamfer angle (second rake angle),  and width of cut, respectively. Note that the cutting forces are predicted from the shear angle evaluated from the minimum energy principle, and the fundamental properties of material while considering the strain, strain rate and temperature. Hence, the proposed model is different than mechanistic models, and it is based on comprehensive extension of analytic approach proposed by Oxley [6].  4.3  M o d e l Verification This section shows the experimental method and demonstrates estimation of the cutting  process variables in high speed machining of P20 mold steel with chamfered tools using the model presented in this chapter. The cutting model developed for the chamfered tools provides  101  Chapter 4. Modeling of Machining with Chamfered Tools  the prediction of cutting process, such as shear angle d>, friction angle 0, cutting energy E , C  cutting forces F and F , and cutting temperature in the primary shear TAB and the tool-chip C  interface T ;  4.3.1  nter  T  zones.  C h a m f e r Tools U s e d i n M a c h i n i n g Tests  Two different cutting tool materials are used in the experiments. The first set was blank carbide ISO S10 tools from S A N D V I K (N151.2-650-50-3B). They were ground to have different chamfer angle (ai) and width (b f) as listed in Table 4.1. Although a range of cutting speed was c  tried, two key cutting speeds (V = 240,600 m/min) are reported with *i = 0.1 mm/rev chip w  load. The second set is MITSUBISHI MB820 Cubic Boron Nitride (CBN) with chamfered edges, see Table 4.2 for tool geometry and cutting conditions. The C B N cutting tests have been conducted at cutting speeds 240,600,1000 m/min with a chip load of t — 0.06 mm/rev.  Table 4.1: Cutting conditions and chamfer geometry for the prepared chamfered edge tools used in machining tests, width of cut w=3.6 mm, main rake angle a = 0 ° . P20 work material: hardness 34 H R C , Composition: C 0.37%, Si 0.3%, M 1.4%, C 2.0%, Ni 1.0%, M 0.2%. S A N D I V I K S10 carbide tool: W C 36.1%, T£ 39.3%, T C 8.6%, C 11.0%. 0  n  r  0  a  Feedrate ti=0.1 mm/rev Cutting speed V^,=240 m/min Tool number b f (mm) ai (deg.)  Feedrate ti=0.1 mm/rev Cutting speed I4,=60( m/min Tool number b (mm) OJI (deg.)  CFT20-02 CFT04 CFT12 CFT15  CFT20-01 CFT02 CFT09 CFT18  c  0.0902 0.1660 0.0841 0.0863  -10° -15° -25° -35°  cf  0.0928 0.0902 0.0896 0.8990  -10° -15° -25° -35°  0  102  Chapter 4. Modeling of Machining with Chamfered Tools  Table 4.2: Cutting conditions and chamfer geometry for the C B N (MITSUBISHI MB820) chamfered edge tools used in machining tests. Average width of cut w=2.55 mm, main rake angle a = - 5 ° . C B N tool material composition: C B N 50%, (T N and Al O ) 50%. 0  t  Tool No.  Undeformed Cutting chip thickness speed i i (mm) V m/min 240 0.06 600 0.06 0.06 1000  bf  Oil  (mm)  (deg)  0.10 0.10 0.10  -25° -25° -25°  c  2  z  w  CBN01 CBN02 CBN03  4.3.2  Predicted and Experimental Results  A series of simulations are carried out using the proposed cutting model for chamfered tools. These results are useful to analyzed the effect of chamfer geometry and cutting conditions on the chip formation in high speed machining of P20 mold steel. To verify the proposed model, some experimental results for both chamfered carbide and C B N tools are compared with the predicted results. The cutting performance in terms of tool wear observed from experiments is compared as well.  Effect of C h a m f e r A n g l e on C u t t i n g  Process  The effect of chamfer angle on the cutting process with S10 chamfered carbide tools is analyzed by the proposed analytic model. The model predicts shear angle, average friction angle on the rake face, and cutting forces, temperature, strain and strain rate in primary, secondary and dead plastic zones. The chamfer length of b f = 0.090mm is used in all model c  simulations, which is equal to an average value of prepared chamfered carbide tools. In all simulations, chamfer angle varies from —5° to —40°.  103  Chapter 4. Modeling of Machining with Chamfered Tools  Vw= 240 m/min, ti =0.1 mm  •  •  Predicted Experimental  Vw = 600 m/min, ti= 0.1 mm  <>  20  40  0  Predicted Experimental  a>  o>32 IS  «30 o W28  10  20  30  40  Chamfer angle a° (a)  30  Chamfer angle a° (C)  Vw= 240 m/min, ti = 0.1 mm  Vw = 600 m/min, ti= 0.1 mm  Predicted  Predicted  £25  20  30  Chamfer angle a , (b)  20 0  30  Chamfer angle a' (d)  Figure 4.5: Effect of chamfer angle on the predicted and experimental shear angles 6 (a), (c)) and predicted friction angles 0 (b), (d) (S10 chamfered carbide tools).  104  Chapter 4. Modeling of Machining with Chamfered Tools  Figure 4.5 shows the predicted shear angles and friction angles versus various chamfer angles at cutting speeds 240, 600 m/min. Experimental shear angle is evaluated from equation 3.43 as demonstrated in chapter 3. Predicted and experimentally evaluated shear angles are in close agreement, and they remain approximately constant regardless of the changes in the chamfer angle. This can be explained by the presence of dead metal zone over the chamfer face, and the dead metal zone forms a shape similar to the sharp cutting edge, which do not change the shearing action in the primary zone. Predicted shear angles show about 2° ~ 3° decrease compared to the predicted shear angles for cutting with sharp tools under the same cutting conditions. However, the friction between the dead metal zone and moving chip creates additional forces. This hypothesis is verified by evaluating the friction angle which increases about 28° at cutting speed 240 m/min, and 26° at cutting speed 600 m/min, when the chamfer angle is changed from —5° to —40° at cutting speed (equation 4.17). In the case of cutting with sharp tools, predicted friction angles remain about 24° for both cutting speed at 240 and 600 m/min (chip load £i=0.1 mm/rev).  Figure 4.6 shows the predicted total cutting forces and chamfer forces against different chamfer angles. Total predicted cutting forces (predicted by equation 4.18) are compared with experimentally measured total tangential (F ) and feed (F ) forces at cutting speeds c  t  240,600 m/min. For an analytical prediction, the agreement between the measured and estimated cutting forces is quite acceptable. Hirao and Tlusty [3] observed from machining tests that although the chips obtained with or without chamfer edges were similar, the total cutting forces were quite different. This can be clearly explained by the physic based analytic model, where the chamfer zone forces (given by equations 4.21) increase with the increasing chamfer angle. Since all cutting conditions are identical except the chamfer angles, the increase in the cutting forces is mainly due to forces contributed by the chamfer zone, see figure 4.6. Chamfer forces in the feed direction (F _ /) have higher amplitudes than the tangential component, t  c  105  Chapter 4. Modeling of Machining with Chamfered Tools  1  1  1  1  i  1  Vw = 240 m/min, ti= 0.1 mm o  11400  Predicted o Experimental  i  i  Vw = 600 m/min, ti = 0.1 mm  o  Predicted o Experimental  ^ 1200  -  0  0  CO  Z  1  1  20  1  i  30 40 Chamfer angle a °  h  i  50  -  S  0 0  cutting  0  —  o  o  800 i  60  i  20  (a)  i 1 30 40 Chamfer angle a ,  1  50  o  60  (c) 1  1  1  Vw = 600 m/min, ti = 0.1 mm  <>  Predicted <> Experimental  <L—-  ^<—* i  20  30 Chamfer angle a,°  (b)  Chamfer angle <x°  (e)  40  10  i  20  i 30 40 Chamfer angle a °  i 50  (d)  Chamfer angle a  1  (f)  Figure 4.6: Effect of chamfer angle a i on the total cutting forces ((a), (b), (c), (d) and chamfer forces ((e), (f)) (S10 chamfered carbide tools).  60  106  Chapter 4. Modeling of Machining with Chamfered Tools  since the pressure on the chamfer face has stronger component in the feed direction as the chamfer angle increases. For the comparison, the cutting (F ) and feed (F ) forces measured c  t  from cutting with S10 carbide sharp tools at cutting speed 240 m/min and undeformed chip thickness t  x  = 0.1 mm are F =817 N and F =390 N, respectively. Similarly, experimentally c  t  measured cutting and feed forces are F =890 N and F = 445 N at cutting speed K,=600 m/min c  t  and undeformed chip thickness ti=0.1 mm. A l l the predicted and measured cutting and feed forces for cutting with chamfer tools are higher than those for cutting with sharp tools.  The effect of chamfer angle on the predicted cutting temperature in the primary shear TAB and the tool-chip interface Ti  nter  zones is shown in figure 4.7. Both predicted temperature rise  in the primary shear and the tool-chip interface zones show little dependency on the variation of chamfer angles. In general, temperature at the tool-chip interface Ti  nter  is about 100 ~ 200° C  higher than that predicted by sharp tools. Since shear angles and friction angles at the tool-chip interface are not affected by the variation of chamfer angles significantly. Therefore, cutting temperature does not vary with chamfer angle significantly when cutting speed and undeformed chip thickness remain constants. The predicted and experimentally evaluated cutting energy E versus chamfer angle is c  shown in figure 4.7. Experimentally determined cutting energy per unit volume is found using same equation 3.65 shown in chapter 3. The same trend as the predicted shear angles against chamfer angles can be seen for the predicted cutting energy. Predicted cutting energy E shows c  little dependency on the variation of chamfer angles. The predicted cutting energy E shows a c  close agreement with that evaluated from experiments.  Effect of C u t t i n g Speed on C u t t i n g  Process  Since C B N tools are more thermal resistant, they are used to evaluate the influence of  107  Chapter 4. Modeling of Machining with Chamfered Tools  400r  1  1  1  Predicted temperature rise in the primary shear zone v>  E  Vw =240 m/min, ti = 0.1 mm  Vw=600 m/min, ti = 0.1 mm  CD 1  3  •  Predicted • Experimental  o  2 360 CO  o. E £ 340o>  E>  Vw =240 m/min, ti = 0.1 mm  CO  c CO  o) 2  c  § 320r  e  10  20  O 1.5  30  Chamfer angle a, (a) ,2000-  CD i_ D  E 3  Vw=600 m/min, ti = 0.1 mm  r  60  50  30 40 Chamfer angle a !  (c)  Predtcted temperature rise at the tool-chip interface  » 1800  20  0  Vw=600 m/min, ti = 0.1 mm •  Predicted • Experimental  40  50  o  ^2.5  2 16001Q.  TO  Vw =240 m/min, ti = 0.1 mm.  I 1400H  CO  c  CO  a 2 c  O)  E  o  •1 120010 ° 1000 L  20  30  o  40  Chamfer angle a," (b)  50  60  1.5  20  30  (d)  Figure 4.7: Effect of chamfer angle a\ on the cutting temperature (TAB, Ti ) and energy (E ) (c), (d), (S10 chamfered carbide tools). nter  c  60  Chamfer angle a,'  (a), (b)  108  Chapter 4. Modeling of Machining with Chamfered Tools  cutting speed on cutting process. The tests were conducted at three cutting speeds: 240, 600, and 1000 m/min with a chamfer geometry: a i = -25°,6 /=0.1 mm. In all simulations, cutting C  speed varies from 240 to 1100 m/min.  Figure 4.8 shows the predicted and experimental shear angles and the predicted friction angles against cutting speed for C B N tools. The predicted and experimentally evaluated shear angles are in close agreement. Again, experimental shear angle is obtained by evaluating the chip ratio as shown in equation 3.43. Both the predicted and experimental shear angles show a slight increase as cutting speed is increased from 240 to 600 m/min. The effect of the further increase of cutting speed on shear angle becomes insignificant. The predicted friction angle decreases from about 19° to 16° when cutting speed is changed from 240 to 1000 m/min. It also can seen that the predicted friction angle increases from 16° to 19° as cutting speed is increased from 600 m/min to 1000 m/min. Experimental evidence suggests that the similar trend is observed for the measured contact length along the tool-chip interface.  Figure 4.9 shows the effect of cutting speed on the predicted and experimentally measured cutting forces (F , F ) and the predicted chamfer forces ( F _ / , F _ ) . The predicted cutting c  c  t  c  t  c /  forces (F , F ) show a good agreement with those measured from experiments. The cutting c  t  forces F and F measured from cutting tests show a little variation with the cutting speed since c  t  the friction at the tool-chip interface varies with cutting speed insignificantly within the cutting speeds V : 240 ~ 1000 m/min. Turning tests with MITSUBISHI chamfered C B N tools at w  cutting speeds 400, 600, 800 m/min also show the similar trend in the machining of P20 mold steel ([70]). The predicted chamfer forces ( F _ / , F _ / ) indicates that chamfer forces seems c  c  t  c  to remain constants when cutting speed is changed from 240 to 1000 m/min. Chamfer forces is predicted by equations 4.21. Again, the predicted chamfer forces (F _ /) in feed direction are t  c  higher than those in cutting direction ( F _ / ) . Machining tests with both chamfered carbide c  c  109  Chapter 4. Modeling of Machining with Chamfered Tools  45 40  o  1 ti  r  = 0.06 mm, en = -25, bcf = 0.1 mm  •  •  Predicted Experimental  -ecn 35  d  CO  c5 30  CD -C  CO  25  200  300  400  _i  500  i  600  i_  i  700  Cutting speed  800  900  1000  1  1  1100  1200  Vw (m/min)  (a) -i  1  o  ti  1  1  1  = 0.06 mm, on = -25, bcf = 0.1 mm  r  Predicted  CD CO  18  T5 16 14 12 200  _i  i  i  i  i  i_  300  400  500  600  700  800  Cutting speed V  w  900  _i  i_  1000  1100  1200  (m/min)  (b)  Figure 4.8: Effect of cutting speed on the predicted and experimental shear angle <j> (a) and predicted friction angle 3 (b) (MB820 C B N chamfered tools).  Chapter 4. Modeling of Machining with Chamfered Tools  z  800  o 700  1  ti = 0.06  1  1  1  1  110  r  i  mm, on = - 2 5 , bcf =0.1 mm  r  Predicted o  Ll_ CD O 600 O  o  Experimental  o> cz 500 '*= Z3 o  o 1—  400 300 200  _i  i  i  i  i  i  i  i  i_  300  400  500  600  700  800  900  1000  1100  1  1  Cutting speed V (a) 8001  1  1—  i  "i  w  n  i  i  0'  700 CD  o  o  ^  CD CD  1200  (m/mi )  ti = 0.06 mm, ai = -25, bcf =0.1 mm A  A  r  Predicted Experimental  600 500  — 400 CO  300 200  j  300  i  i_  400  500  600  700  Cutting speed V (b)  200  300  400  500  600  700  800 w  900  1000  1100  1200  900  1000  1100  1200  (m/min)  800  Cutting speed V« (m/min) (c) Figure 4.9: Effect of cutting speed V on the total cutting forces ((a), (b)) and chamfer forces (c) (MB820 C B N chamfered tools). w  111  Chapter 4. Modeling of Machining with Chamfered Tools  and C B N tools show this characteristic.  The effect of cutting speed on the predicted cutting temperature in the primary shear and the tool-chip interface zone is shown in figure 4.10. It can be seen that although the predicted temperature rise is only about 50° in the primary shear zone, temperature in the tool-chip interface increases from 1100° to 1700° when cutting speed is increased from 240 m/min to 600 m/min. The effect of temperature rise in tool-chip interface zone on the tool wear will be discussed later. As discussed in chapter 3, cutting speed has profound effect on the cutting temperature at the tool-chip interface T  . Figure 4.10 (c) shows the effect of cutting speed on  inter  the predicted and experimentally evaluated cutting energy E . The predicted and experimental c  cutting energy are in close agreement at cutting speed range: 240 m/min ~ 1000 m/min. Since shear angle and cutting forces are not changed significantly when cutting speed is increased from 240 m/min to 1000 m/min, both the predicted and experimental cutting energy E remain c  nearly constants.  Observation of Tool W e a r  It is of interest to evaluate the wear behavior of chamfered tools with different chamfer geometry and compare it with sharp tools. Tool wear tests have been performed and the chamfered tools used in tool wear tests and cutting conditions are given in Tables 4.1 and 4.2.  Tool wear tests have been carried out to investigate the effect of chamfer angle and cutting speed on the tool wear Vg. Figure 4.11 (a), (b) show the comparison of tool wear VB of S10 carbide tools with different chamfer angles at cutting speed 240 m/min and 600 m/min. Figure 4.11 (c) shows the effect of cutting speed on the tool wear of chamfered C B N tools. It is reported that the diffusion temperature for Cobalt binding material used in S10 carbide tools is about  112  Chapter 4. Modeling of Machining with Chamfered Tools  o 450  1  1  1  1  1  1  1  1  r  Predicted temperature rise in the primary shear zone  CD CD =3  400  25  g_350 CD CD  ti = 0.06 mm, ai =- 25 , bcf = 0.1 mm  ~ 300 O  i_  j  200  300  400  J  500  i  i  i  600  700  800  Cutting speed V i  2000 CD  i  1000  i  1100 1200  (m/min)  w  (a)  o  H-  i  900  i  i  i  i  i  i  i  r  Predicted temperature rise at the tool-chip interface  1800  3 1600 Co CD  a . 1400 E CD  b = 0.06 mm, cci =- 25 , bcf = 0.1 mm  T11200 CO  oc:  J  200 1000  300  L  400  500  600  700  Cutting speed V (b)  800 w  900  E .E  1100 1200  ( /min) m  b = 0.06 mm, ai =- 25 , bcf = 0.1 mm  m  1000  Predicted  Experimental  0 2.5 LLI >-. Oi CD £= CD CD o CZ 2  O  1.5  200  300  400  500  600  700  800  900  1000  1100  Cutting speed Vw (m/min) (c)  Figure 4.10: Effect of cutting speed V on the predicted cutting temperature in the primary shear and the tool-chip interface zones ((a), (b)), the predicted and experimental cutting energy (c) (MB820 C B N chamfered tools). w  113  Chapter 4. Modeling of Machining with Chamfered Tools  t, = 0.1 mm, Vw= 240m/mn i ( carbide ) T  Chamfer angle <x°  (a )  t,= 0.1 mm,V = 600 m/mn i ( carbide ) w  i i  JHk. - i _!_J T00LM  0.35  a L  I S  0.2  T  0.15  1 1  i i  0.1  i i i  0.05  i i  -1  u  1 1 1 1  — r — i — -  j * *j  1  i i  X 1 1  _i  \ - i • •« —  ' i  1 1  -  r  1 II 1  •  1 1  Ji i i  r i i i  * i i i  i i  —  i  r  i i ~ ii ii i  Ti ii i  20  —  i :: i i  15  i i  —  T  T  10  i i  i i  r  30  Chamfere angle o°  (b)  i ii i  35  ti = 0.06 mm, cxi=-25,°b <*= 0.1 mm ( CBN ) I  I  L TOOL>x!  1  1  |  |  i  i i  ~ *  i i  i i i  r  \  0.05 -  200  >^ i-  i  A  3O0  400  —  h" *  500  i i i i  1  i  i L L.- A L.. i 1 i li i | L L_. L L_. ii 1 1 1 i 1 1 i —  I—  \b[cf>  1  \  600  1  L  700  Cutting speed V  800  (m/min)  i i i i i i i i 900  1 i  ii i i i i i  i  1000  i  r  i  1 i i  ii 1100  1200  :c) Figure 4.11: Comparison of tool wear Vg for chamfered carbide (a), (b), and C B N (c) tools from machining tests. w  Chapter 4. Modeling of Machining with Chamfered Tools  1300°C and 1600°C for binding material (Al 0 ) 2  3  114  used in C B N tools [72]. Hence, ISO S10  carbide tool must be used under 1300° C. It means that cutting speed should be selected under 240 m/min for machining P20 mold steel with S10 carbide tools. C B N may sustain without diffusing its binding materials up to 600 m/min. When the chamfer angle of the carbide tool is varied from 0° (i.e. sharp cutting edge) to —35°, the minimum wear was obtained with tools which had —15° chamfer angle. Larger chamfer angles increased the force and friction, and smaller chamfer angles weaken the wedge, hence causing more flank wear. The trend was the same at both cutting speeds (240, 600 m/min). However, for the same volume of the material removed, the 240 m/min cutting speed gave 6 times lower flank wear than the cutting speed 600 m/min where severe crater wear due to diffusion of Cobalt binding was observed. While S E M pictures showed frequent micro-cracks and chipping in sharp cutting edges, there were no damage on the tools with —15° chamfer angle used at 240 m/min cutting speed. Evidently, 240 m/min speed corresponds to about 1300° C temperature on the rake face, which is just below the melting temperature of P20 and diffusion of Cobalt binding within the ISO S10 carbide tool. Hence, both analytic model and experiments indicate that ISO S10 carbide tools with chamfer angle is —15° at 240 m/min must be used in continuous machining of P20 mold steels at dry cutting conditions. For tool wear tests using chamfer C B N tools, it shows that tool wear is proportional to the increase of cutting speed as seen figure 4.11 (c) since higher cutting speed causes higher temperature rise at the tool-chip interface. Compared to the S10 carbide tools, much higher speeds (500m/min) can be used with C B N tools since C B N tools did not exhibit significant crater wear and microcracks up to 600 m/min cutting speed.  Figure 4.12 and 4.13 show the comparison of variation of tool wear VB with cutting length between a sharp edge tool and a chamfered tool with —15° chamfer angle at the cutting conditions: ti=0.1 mm, K,=240 and 600 m/min, respectively. A chamfered tool with —15° chamfer  115  Chapter 4. Modeling of Machining with Chamfered Tools  Cutting conditions:  Sharp edge tool Chamfered edge tool  t,=0.1 mm, V =240 m/min  1  Chaml er geometris: /  a - 1 5°, b =0.16 6 mm 1=  L3  /  cf  y  /  /•  ^ E  0 /  ;  • r/  r  j  / /  /  : /  20  40  60 80 Cutting distance (m)  100  120  140  Figure 4.12: Comparison of tool wear history between a chamfered tool with —15° chamfer angle and a conventional sharp tool ( S A N D V I K carbide tools).  Chapter 4. Modeling of Machining with Chamfered Tools  116  angle at the cutting speed of 240 m/min shows the development of tool wear is nearly two times lower than that of a sharp tool, much lower than that of sharp tool at the cutting speed of 600 m/min.  4.3.3  Summary  Mechanics of cutting with chamfered tools is presented in this chapter. The proposed model extends the analytic approach of Oxley et al. [6], [36] to chamfered tools. The plastic deformation zones are divided into primary shear zone, secondary deformation zone where the chip moves over the regular rake face, and the chamfered edge zone where the metal is trapped by forming a dead metal zone. An extrusion model is applied to the trapped metal zone. In all three zones, the yield and flow stress of the material are expressed as a function of strain, strain rate and temperature whose relationships are obtained from orthogonal cutting tests. The proposed model predicts the cutting forces and temperature in each deformation zone with realistic results. The model thus allows the analysis of how chamfer geometry and cutting speed influence the cutting performance, such as forces, temperature and tool wear. With the aid of proposed model, it has been observed that the optimal chamfer angle is —15° and the cutting speed is 240 m/min when dry cutting P20 mold steels with carbide tools. The same material can be cut up to 600 m/min with chamfered C B N tools.  Chapter 4. Modeling of Machining with Chamfered Tools  117  Figure 4.13: Comparison of the tool wear history between a chamfered tool with —15° chamfer angle and a conventional sharp tool ( S A N D V I K carbide tools).  Chapter 5  Conclusions  The objective of this thesis was to investigate the effects of tool edge geometry and cutting conditions on the machining of hardened steels. Analytical models have been developed for orthogonal machining, where sharp and chamfered cutting tools are modeled to investigate the influence of tool geometry and cutting conditions on cutting force and temperature for machinability analysis. The mechanics of machining hardened mold steels are studied for both sharp edge and chamfered cutting tools. First, the cutting forces and temperature are predicted for machining with sharp tool, using Oxley's slip line field model [6]. The flow stress of the material is identified directly from orthogonal cutting tests where the shear angle, average friction coefficient, temperature, shear stress, strain and strain rate are estimated from material properties, measured chip thickness, rake face-chip contact length and cutting forces. Oxley et al.[6] used high speed compression test data to evaluate the flow stress, as opposed to orthogonal cutting test data proposed in this thesis. The analytical model is used to predict the cutting forces, shear angle, flow stresses and temperature on both primary shear and chip-tool rake face contact zones. The predicted results are compared with measurements from orthogonal cutting tests conducted with sharp ISO S10 carbide tools. The work material used in experiments was P20 mold steel. The following observations are made from the results:  • The strain hardening index evaluated from orthogonal cutting tests with sharp tools indicate that the strain hardening decreases with increasing speed. Experimental observation 118  Chapter 5.  Conclusions  119  also suggests that strain hardening becomes insignificant when cutting speed reaches a certain value. • The temperature rise at the tool-chip interface mainly depends on the cutting speed. Predicted temperature rise in the primary shear zone is not significant at the speed range tested. However, the predicted temperature rise at the tool-chip interface is close to the melting temperature of P20 mold steel and diffusion temperature of Cobalt binding of the ISO S10 carbide tool at about cutting speed 300m/mm. Higher cutting speeds which cause to temperature beyond the diffusion limit of the carbide tool, leads to significant crater wear in the machining experiments. • The model was found to be useful in analyzing optimal cutting speeds and chip loads in continuous turning of P20 mold steels. Mechanics of cutting with chamfered tools has been modeled by extending the slip line field from the primary and the secondary deformation zones to the dead metal zone trapped over the chamfer land. The dead metal zone is assumed to be formed as the continuation of the primary shear line towards the cutting edge. As suggested by the experimental observations reported in the literature, the trapped metal is assumed to stay stationary and form a natural cutting edge as the continuation of the main rake face. The metal flow at the boundary of the dead metal is modeled similar to an extrusion process, where the boundary is assumed to act like a die wall. The contact between the chip and the main rake face is assumed to have an equal mixture of sticking and sliding zones. The total strain and friction energy produced in the primary, secondary and dead chamfer zones are formulated. The shear angle in the primary shear zone is predicted by minimizing the total energy consumed in chip formation. The proposed model predicts stresses, forces, temperature, and strain, strain rate and temperature dependent flow stress in the primary shear zone, dead metal boundary and at the chip - rake face contact area. The prediction results compared favourably with the experimental measurements conducted with chamfered ISO  Chapter 5.  Conclusions  120  S10 carbide and MITSUBISHI C B N cutting tools used in orthogonal turning of P20 mold steels.  The following conclusions are drawn from the chamfered cutting tool model and experimental results: • Predicted and experimentally determined shear angles indicate that chamfer does not change the shearing process in the primary shear deformation zone significantly. Friction angles at the tool-chip interface, the cutting energy consumed, and cutting temperature rise in the primary shear deformation and tool rake face - chip interface zones show similar trends. However, predicted and experimentally measured cutting forces increased with the increasing chamfer angle, which is attributed to the presence of pressure and friction load at the dead metal - metal flow interface over the tool chamfer. Since the pressure on the dead metal interface coincides with the feed direction, the feed forces increase more than the tangential forces as the chamfer angle is increased. • C B N tools seem to have a lower coefficient of friction than ISO S10 carbide tools. The friction coefficient for ISO S10 carbide tools varied from 28° to 26° as the cutting speed increased from 240 to 600 m/min, which resulted in an average shear angle of about 30°. When the cutting speed is varied from 240 to 1000m/min with the C B N tools, the friction angle varied from only 16° to 19°. Therefore, the predicted and experimental shear angle and cutting energy did not also exhibit noticeable change within the cutting speed ranges tested. Furthermore, the cutting forces did not change significantly within the cutting speed ranges of 240m/min to 1000m/min. The predicted temperature indicates that the P20 material already reaches its re-crystallization phase (1000° (7,7 region in Fe-C phase diagram) at the cutting speed 240m/min as the chamfered tools were used in cutting tests. Therefore, there is no strain hardening to cause a force increase in the secondary zone beyond this speed.  Chapter 5.  121  Conclusions  • The temperature at the chip - tool interface reaches the diffusion limit of binding materials within the tool. This limit is about 1300° C at the cutting speed of 240m/min for chamfered ISO S10 carbide tools, and 1600°C at the cutting speed of 600m/mm for chamfered C B N tools. Accelerated crater wear has been observed beyond these cutting speeds due to the diffusion of binding materials Cobalt and Al 0 2  3  for carbide and C B N  tools, respectively. • In addition to cutting speed, the tool wear experiments indicate that the chamfer angle has a strong influence on the tool wear. When chamfer angle is varied from 0° to —35° on carbide tools, the minimum tool wear is observed around chamfer angle —15°. Larger chamfer angles increase the force and friction, and smaller chamfer angles weaken the wedge of cutting tools, hence, causing more tool wear. When the same volume of material was removed, the cutting speed at 240 m/min gave about 6 times lower flank wear than the cutting speed 600 m/min, where severe crater wear due to diffusion of Cobalt binding was observed. C B N tools with —25° chamfer angle outperformed the C B N tools with —35° chamfer angle. Furthermore, the Scanning Electron Microscope (SEM) results of C B N tools with —35° showed a significant amount of micro-crack both within the C B N material and CBN-carbide bonding interface at the cutting speed of 800 m/min in turning tests. This thesis presents a useful analytical model in analyzing the influence of tool geometry and cutting conditions in high speed machining of hardened steels. The model can be used for other materials cut at a wide speed range. 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Arsecularatne, 1997, " On Tool-Chip Interface Stress Distribution, Ploughing Force and Size Effect in Machining International Journal of Machine Tool Manufacturing, Vol.37, No.7, pp885-899. [42] H. Berns, J. Liu and W. Theisen, 1996," A New Experimental Approach to Metal Cutting Z.Metallkd, Vol.87, No.5. [43] E J . A . Armarego and R.H. Brown, 1969, The Machining of Metal, Prentice-Hall Inc.. [44] A . Ghosh and A . K . Mallik, 1986, Manufacturing Science, Ellis Horwood Limited. [45] E.M. Trent, 1991, Metal Cutting, Third edition, Butterworth-Heinemann Ltd. [46] K. Hitomi, 1961, " Fundamental Machinability Research in Japan ", Journal of Engineering for Industry, November, pp531-544. [47] S. Jacobson and P. Wallen, 1988, " A New Classification System For Dead Zone in Metal Cutting ", International Journal of Machine Tools Manufacturing, Vol.28, No.4, pp529-538. [48] H.K. Tonshoff, W. Bussmann and C. Stanske, 1986, " Requirements on Tools and M a chines When Machining Hard Materials ", Proceedings of the 26th International Machine Tool Design and Research Conference, September, pp349-357. [49] E. Usui, K. Kikuchi and K. Hoshi, 1964," The Theory of Plasticity Applied to Machining with Cut-Away Tools ", Journal of Engineering for Industry, Transaction of A S M E , May, pp95-104. [50] H.T. Zhang, P.D. Liu and R.S. Hu, 1991, " A Three Zone Model and Solution of Shear Angle in Orthogonal Machining ", Wear, Vol.143, pp29-43. [51] B. Avitzur, 1968, Metal Forming: Process and Analysis, McGraw-Hill Book Company. [52] H. Kudo, 1965, " Some New Slip-Line Solutions for Two-Dimensional Steady-State Machining ", International Journal of Mechanical Science, Vol.7, pp43-55. [53] W.F. Hosford and R.M. Caddell, 1993, Metal Forming Mechanics and Metallurgy, PTR Prentice-Hall Inc.. [54] D. Dudzinski and A . Molinari, 1997," A Modeling of Cutting for Viscoplastic Materials ", International Journal of Mechanical Science, Vol. 39, No. 4, pp369-389.  Bibliography  127  [55] R.F. Recht, 1985," A Dynamic Analysis of High-Speed Machining ", Journal of Engineering for Industry, Vol. 107, November, pp309-315. [56] J.S. Strenkowski and J.T. Carroll, 1985, " A Finite Element Model of Orthogonal Metal Cutting Journal of Engineering for Industry, Vol. 107, pp349-354. [57] K. Komvopoulos and S.A. Erpenbeck, 1991, " Finite Element Modelling of Orthogonal Metal cutting ", Journal of Engineering for Industry, Vol. 113,pp253-267. [58] T.D. Marusich and M. Ortiz, 1995," Modeling and Simulation of High-Speed Machining ", International Journal of Numerical Methods in Engineering, Vol. 38, pp3675-3694. [59] R.A.C. Slater, 1977, Engineering Plasticity - Theory and Application to Metal Forming Process, THE MACMILLAN PRESS LTD. [60] P.W. Wallace and G. Boothroyd, 1964," Tool Forces and Tool-Chip Friction in Orthogonal Machining ", Journal of Mechanical Engineering Science, Vol. 6, No. 1, pp74-87. [61] W.B. Palmer and P.L.B. Oxley, 1959, " Mechanics of Orthogonal Machining ", Proceedings Institution of Mechanical Engineers, Vol. 173, No. 24, pp623-654. [62] M.G. Stevenson and P.L.B. Oxley, 1970-1971, " An Experimental Investigation of the Influence of Strain-Rate and Temperature on the Flow Stress Properties of a Low Carbon Steel Using a Machining test ", Proceedings Institution of Mechanical Engineers, Vol. 185,pp741-754. [63] Modern Metal Cutting - A Practical Handbook, AB Sandvik Coromant, Technical Editorial Department, Sweden, 1994. [64] M.I. Sadik and B. Lindstrom, 1993, " The Role of Tool-Chip Contact Length in Metal Cutting Journal of Materials Processing Technology, Vol 37, pp613-627. [65] T.C. Hsu, 1966," A Study of the Normal and Shear Stress on a Cutting Tool ", Journal of Engineering for Industry, February, pp51-64. [66] M.ES. Abdelmoneim and R.F. Scrutton, 1974," Tool Edge Roundness and Stable Buildup Formation in Finish Machining ", Journal of Engineering for Industry, November, ppl258-1267. [67] T.I. Elwardany, E. Mohammed and M.A. Elbestawi, 1996, " Cutting Temperature of Ceramic Tools in High Speed Machining of Difficult-to-cut Materials International Journal of Machine Tools Manufacturing, Vol. 36, No. 5, pp611-634. [68] W. Johnson, 1979, " Applications: Processes Involving High Strain Rates ", Institution of Physics Conference, Series No. 47: Chapter 4, pp337-357.  Bibliography  128  [69] Xiaoping L i , 1997, " Development of a Predictive Model for Stress Distributions at the Tool-Chip Interface in Machining ", Journal of Materials Processing Technology, 63, ppl69-174. [70] F. Vygen, "Characteristics of Tool Wear in High Speed Machining of P20 Mold Steel using C B N and Carbide Tools ", Diploma thesis, visiting student in the Manufacturing Automation Laboratory at UBC, Technological University of Munich, Germany, 1998. [71] LH.Weiner, 1955, "Shear-Plane Temperature Distribution in Orthogonal Cutting", Trans. ASME 77,ppl331-1341. [72] A S M International Handbook Committee, 1989, Metal Handbook Ninth Edition, Vol. 16, ASM,pp71-117. [73] A . O . Tay, M.G. Stephensen, G. De Vahl Davis, and P.L.B. Oxley, 1976, " A Numerical Method for Calculating Temperature Distributions in Machining, from Force and Shear Angle Measurements ", International Journal of Machine Tool Design and Research, Vol. 16, pp335-349. [74] D. Kececioglu, 1960," Shear-Zone Size, Compressive Stress, and Shear Strain in MetalCutting and Their Effects on Mean Shear-Flow Stress ", Journal of Engineering for Industry, February, pp79 - 86.  Appendix A  T e m p e r a t u r e i n the P r i m a r y Shear a n d the T o o l - C h i p Interface Zones  M a t e r i a l t h e r m a l properties of P 2 0 m o l d steel  The thermal properties, heat conductivity (K) and specific heat (c) for P20 mold steel is given by the material handbooks as: K  =  28.74 + 0.0053T (J/ms°C)  pc  =  3.59 x 10 - 100T ( J / m C ) 6  3 o  C a l c u l a t i o n of t e m p e r a t u r e i n t h e p r i m a r y shear zone  The temperature in the primary shear zone T  is determined by considering the plastic  AB  work done in this zone and is given by rp rp , (1 i-AB = J-room + 1] 7  \ )F cosa 7, T s  s  0  (A.l)  pct\w cosyp — a ) 0  where F , 6, a , and ti are shear force on AB, shear angle, tool rake angle, and undeformed s  0  chip thickness, respectively. T  room  is the initial temperature of work material. Based on heat  partition principle, Boothroyd [19] suggested that a coefficient (A ) can be used to determine g  the proportion of heat conducted into the workpiece in the primary shear zone. It is found that A is a function of RTtan6 . Oxley et al. [6], [36], [62] proposed empirical equations to g  s  calculate \ , which is closed to the results reported by Weiner's [71] energy partition function. s  X  s  X  s  = 0.5 - 0.35logi (R tan6) 0  =  T  0.3 - 0.15log (R tan6) 1Q  T  129  for  0.04<R tan6<10.0 T  for R tan6> 10.0 T  (A.2)  Appendix A. Temperature in the Primary Shear and the Tool-Chip Interface Zones 130  Where R is non-dimensional thermal number given by R T  T  =  P ^ cyr  Calculation of temperature i n t h e tool-chip interface zone  Oxley et al. [6], [36] proposed that the temperature rise at the tool-chip interface  (r,„ ) is ter  determined by Tinter =  AT  =  C  T{ + 0 . 9 A T  M  Ff sind) c  pctiw cos(d> — a ) 0  (A.3)  Ff  c  ^ o ( ^ )  = R sind a  =  where T, = {T , T }. AB  ti w sin3 sind) cos9  0.06 - 0 . 1 9 5 6 ^ + 0 . 5 l o  9 l 0  For cutting with sharp tools, T, = T .  CF  AB  (^) For cutting with  chamfered tools, T, = T / . t , 5, l is the chip thickness, thickness of plastic zone along the c  2  c  tool-chip interface, and the contact length along the tool-chip interface, respectively. ATM is the maximum rise of temperature along the tool-chip interface. AT is the average temperature C  rise in the chip due to frictional work. In the calculation of average temperature in the tool-chip plastic deformation zone, the ratio of ATM to AT is required as proposed by Broothroyd [19]. C  Stevenson and Oxley [62] applied Broothroyd's analysis and obtained an empirical equation as shown above to determine the ratio of ATM to AT . C  !  Appendix  B  M a p p i n g F l o w Stresses i n t h e machining  E v a l u a t i o n o f flow s t r e s s i n p r i m a r y d e f o r m a t i o n  process  zone  As presented in chapter 3, the flow stress <TI and strain hardening index n in the primary shear deformation zone are mapped from the shear strain *y  AB  and shear strain rate j .  empirical correlation of a and strain hardening index n with shear strain j  AB  x  rate j  AB  AB  A  and shear strain  is obtained from orthogonal machining tests under a range of cutting condition shown  as follows For ti < 0.03 mm CT  X  10864.4399 j °  =  -1.385  j  on  A B  AB  (MPa) (B.4)  n  = 0.00866 j  2.476  j  0 0014 A B  AB  For ti > 0.03 mm  (7!  =  -0.65497  1850.1639  J° JAB  10.17495  r °B ™lAB  178  AB  (MPa) (B.5)  n  Flow tion  h  2.67378  A  VUi  s t r e s s e s (a = {cr f, ai }) c  nter  in the chamfered  zone  131  a n d secondary  deforma-  Appendix B. Mapping Flow Stresses in the machining process  132  Again, the following expressions are calibrated from orthogonal cutting tests with sharp tools, where flow stresses in the primary and secondary zones and their corresponding velocity modified temperature are calculated (see, experimental modeling in chapter 3). Hence, the mapping relation between flow stress and velocity modified temperature T is obtained by m  T  m  < 481.0 (K)  481.0 <T < m  a = 2732.126 - 4.87 T (Mpa) m  730.0 (i^T)  a = -0.6596 10~ T + 0.10957 4  m  T  m  - 59.18 T  m  + 10821.129  (B.6)  (MPa)  T  m  > 730.0 (A")  -> a = 260.0 (MPa)  The velocity modified temperature in chamfered edge (T ) mcf  and tool-chip interface zone  (T ) are given by mtc  Tmcf =  ( T + 273)(1 - 0.09/o (e ))  Tmtc =  (2<„ r  c/  t e  5lo  c/  + 273)(l - 0 . 0 9 / o ^ ^ ) ) 1  (B.7) (B.8)  Appendix C  Identification of E d g e Forces  A schematic diagram for the identification of edge force components in cutting and feed directions, experimental shear stress, shear angle, friction angle, and cutting force coefficients is shown in figure C . l . To identify the edge forces, cutting forces F , F which correspond a c  t  range of undeformed chip thickness ti are required at different cutting speeds. A C program is developed to achieve experimental identification of edge force components. Once a data file , which contains a set of undeformed chip thickness t , and corresponding chip thickness r , 2  x  width of cut w, measured cutting forces F , F , and rake angle a is loaded to the program, the c  t  ot  edge forces are found using the least square root method as shown in figure C . l . Once edge force components F and F , shear angle d>, and friction angle 3 are identified, experimental ce  te  shear stress k A B and cutting force coefficients K  tc  and K  fc  can be determined by following  equations k B A  =  K  =  tc  [(F  - F )cosd) - (F - F )sind>]sind> ti w  c  f  ce  AB  t  te  cos(3 — a ) 0  (C.9)  sind) cos (d) + 8 — a ) a  k B sin(8 - a. ) sind) cos(d> + 3 — a ) A  0  0  The total cutting force F and feed force F can be expressed as c  t  F  c  = F  ce  +  K tw tc x  (CIO)  F  t  = F  u  + Kfchw  133  t  Appendix C. Identification of Edge Forces  Input data file  134  Fitting by least square toot  Measured cutting and leed feces Fc and Ft corresponding undeformed chip thickness 1t  Fc » Fee + A Ft=Fte+  Calculating  ti  shear stress k w  Bti  Cutting force coefficients  Calculating shear angle <> j and Iriction angle p" for each corresponding ti  Measured chip thickness t2 and corresponding ti  Ktc and Kfc  Estimation of cutting forces  i  Fc - Fee + Klc ti w Ft ** Fio + Ktc ti w  Figure C . l : Experimental identification of edge force components From experimental observations, edge forces vary with the cutting speeds. Albrecht [32] also stated this from his experimental observations. Both F  ce  and F are found to decrease te  with the increase of cutting speed V . w  Under the cutting conditions:V = 100, 240, 380, 600 m/min, and w=3.6 mm, the correW  sponding edge forces, F  ce  and F are calculated from the developed program. A empirical te  equation used to determine edge force components F  ce  and F at different cutting speed is te  obtained as shown by equation C . l l F  =  0.4318 x 1 0 - K ,  2  ce  F  =  0.4919 x 1 0 - K ,  2  te  3  3  -  0.53524 V  -  0.7225 V  w  w  + 276.67  (C.ll)  + 352.71  It is noted that equation C . l l is valid for cutting carbide tool (SANDVIK, S10, seefigure3.8).  Figure C.2: Plot of variation of edge forces with cutting speed Figure C.2 shows the variation of edge forces with cutting speeds. For C B N tools, edge forces are given by F F  u  c e  = 80.0  (AO  (C.12)  = 180.0 (iV)  (C.13)  

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