Geometry of Single-point Turning Tools and Drills
Fundamentals and Practical Applications
Viktor P. Astakhov
Contents
1 What Does It Mean “Metal Cutting”? .1
1.1 Introduction .1
1.2 Known Results and Comparison with Other Forming Processes 2
1.2.1 Single-shear Plane Model of Metal Cutting .2
1.2.2 Metal Cutting vs. Other Closely Related Manufacturing
Operations .5
1.3 What Went Wrong in the Representation of Metal Cutting? .22
1.3.1 Force Diagram 23
1.3.2 Resistance of the Work Material in Cutting .25
1.3.3 Comparison of the Known Solutions for the Single-shear
Plane Model with Experimental Results .27
1.4 What is Metal Cutting? 28
1.4.1 Importance to Know the Right Answer 28
1.4.2 Definition .28
1.4.3 Relevance to the Cutting Tool Geometry .29
1.5 Fundamental Laws of Metal Cutting .32
1.5.1 Optimal Cutting Temperature – Makarow’s Law 32
1.5.2 Deformation Law .35
References 50
2 Basic Definitions and Cutting Tool Geometry,
Single Point Cutting Tools 55
2.1 Basic Terms and Definitions .55
2.1.1 Workpiece Surfaces .57
2.1.2 Tool Surfaces and Elements 57
2.1.3 Tool and Workpiece Motions .57
2.1.4 Types of Cutting 58
2.2 Cutting Tool Geometry Standards .60
2.3 Systems of Consideration of Tool Geometry 61
2.4. Tool-in-hand System (T-hand-S) 64xviii Contents
2.4.1 Tool-in-hand Coordinate System .64
2.4.2 References Planes 66
2.4.3 Tool Angles 68
2.4.4 Geometry of Cutting Tools with Indexable Inserts 74
2.5 Tool-in-machine System (T-mach-S) 84
2.5.1 Angles 84
2.5.2 Example 2.3 .88
2.6 Tool-in-use System (T-use-S) .90
2.6.1 Reference Planes 91
2.6.2 The Concept .92
2.6.3 Modification of the T-hand-S Cool Geometry .92
2.6.4 Kinematic Angles .98
2.6.5 Example 2.4 .100
2.7 Avalanched Representation of the Cutting Tool Geometry
in T-hand-S 102
2.7.1 Basic Tool Geometry .102
2.7.2 Determination of Cutting Tool Angles Relation
for a Wiper Cutting Insert 108
2.7.3 Determination of Cutting Tool Angles
for a Single-point Tool .110
2.7.4 Flank Angles of a Dovetail Forming Tool .117
2.7.5 Summation of Several Motions 119
References 125
3 Fundamentals of the Selection of Cutting Tool Geometry Parameters .127
3.1 Introduction .127
3.2 General Considerations in the Selection of Parameters
of Cutting Tool Geometry .129
3.2.1 Known Results .129
3.2.2 Ideal Tool Geometry and Constrains 130
3.2.3 Practical Gage for Experimental Evaluation of Tool Geometry .132
3.3 Tool Cutting Edge Angles .132
3.3.1 General Consideration 132
3.3.2 Uncut ChipT in Non-free Cutting 134
3.3.3 Influence on the Surface Finish 142
3.3.4 Tools with κr > 90° .144
3.3.5 Tool Minor Cutting Edge Angle 147
3.4. Edge Preparation .161
3.4.1 General .161
3.4.2 Shape and Extent 163
3.4.3 Limitations .163
3.4.4 What Edge Preparation Actually Does .169
3.5 Rake Angle 171
3.5.1 Introduction 171
3.5.2 Influence on Plastic Deformation and Generazliations 175Contents xix
3.5.3 Effective Rake Angle .183
3.5.4 Conditions for Using High Rake Angles 189
3.6 Flank Angle .191
3.7 Inclination Angle .193
3.7.1 Turning with Rotary Tools .195
3.7.2 Helical Treading Taps and Broaches 197
3.7.3 Milling Tools 198
References 201
4 Straight Flute and Twist Drills .205
4.1 Introduction .205
4.2 Classification .206
4.3 Basic Terms .208
4.4 System Approach 211
4.4.1 System Objective .212
4.4.2 Understanding the Drilling System 212
4.4.3. Understanding the Tool 212
4.5. Force System Constrains on the Drill Penetration Rate 213
4.5.1 Force-balance Problem in Conventional Drills 213
4.5.2 Constrains on the Drill Penetration Rate 218
4.5.3 Drilling Torque 219
4.5.4 Axial Force .220
4.5.5 Axial Force (Thrust)-torque Coupling .221
4.6 Drill Point 223
4.6.1 Basic Classifications 223
4.6.2 Tool Geometry Measures to Increase the Allowable
Penetration Rate 224
4.7 Common Design and Manufacturing Flaws 259
4.7.1 Web Eccentricity/ Lip Index Error .260
4.7.2 Poor Surface Finish and Improper Tool Material/Hardness .261
4.7.3 Coolant Hole Location and Size .263
4.8 Tool Geometry 267
4.8.1 Straight-flute and Twist Drills Particularities 269
4.8.2 Geometry of the Typical Drill Point 270
4.8.3 Rake Angle .272
4.8.4 Inclination Angle .280
4.8.5 Flank Angle 281
4.8.6 Geometry of a Cutting Edge Located at an Angle
to the y0-plane 292
4.8.7 Chisel Edge 295
4.8.8 Drill Flank is Formed by Two Planes: Generalization .306
4.8.9 Drill Flank Angle Formed by Three Planes .310
4.8.10 Flank Formed by Quadratic Surfaces .313
4.9 Load Over the Drill Cutting Edge .324xx Contents
4.9.1 Uncut Chip Thickness in Drilling 325
4.9.2 Load Distribution Over the Cutting Edge 327
4.10 Drills with Curved and Segmented Cutting Edges 328
4.10.1 Load of the Cutting Part of a Drill with Curved Cutting Edges .329
4.10.2 Rake Angle .332
References 337
5 Deep-hole Tools 341
5.1 Introduction .341
5.2 Generic Classification of Deep-hole Machining Operations .343
5.3 What Does ‘Self-piloting Tool’ Mean? .345
5.3.1 Force Balance in Self-piloting Tools 345
5.4 Three Basic Kinematic Schemes of Drilling .350
5.4.1 Gundrill Rotates and the Workpiece is Stationary .351
5.4.2 Workpiece Rotates and the Gundrill is Stationary .352
5.4.3 Counterrotation 352
5.5 System Approach 353
5.5.1 Handling Tool Failure 353
5.5.2 System Considerations .354
5.6 Gundrills 362
5.6.1 Basic Geometry 362
5.6.2 Rake Surface 365
5.6.3 Geometry of Major Flanks .370
5.6.4 System Considerations in Gundrill Design 390
5.6.5 Examplification of Significance of the High MWF Pressure
in the Bottom Clearance Space 423
5.6.6 Example of Experimental Study 425
5.6.7 Optimization of Tool Geometry .439
References 440
Appendix A
Basic Kinematics of Turning and Drilling .443
A.1 Introduction .443
A.2 Turning and Boring .444
A.2.1 Basic Motions in Turning .444
A.2.2 Cutting Speed in Turning and Boring 448
A.2.3 Feed and Feed Rate 448
A.2.4 Depth of Cut .449
A.2.5 Material Removal Rate 449
A.2.6 Resultant Motion 450
A.3 Drilling and Reaming 450
A.3.1 Basic Motions in Drilling .450
A.3.2 Machining Regime .451
A.4 Cutting Force and Power .453Contents xxi
A.4.1 Force System in Metal Cutting .453
A.4.2 Cutting Power 454
A.4.3 Practical Assessment of the Cutting Force .455
References 461
Appendix B
ANSI and ISO Turning Indexable Inserts and Holders .463
B.1 Indexable Inserts .463
B.1.1 ANSI Code .464
B.1.2 ISO Code 471
B.2 Tool Holders for Indexable Inserts (Single Point Tools) 491
B.2.1 Symbol for the Method of Holding Horizontally Mounted
Insert – Reference Position (1) 492
B.2.2 Symbol for Insert Shape – Reference Position (2) .493
B.2.3 Symbol for Tool Style – Reference Position (3) 493
B.2.4 Letter Symbol Identifying Insert Normal Clearance –
Reference Position (4) 494
B.2.5 Symbol for Tool Hand – Reference position (5) 494
B.2.6 Symbol for Tool Height (Shank Height of Tool Holders
and Height of Cutting Edge) – Reference Position (6) .494
B.2.7 Number Symbol Identifying Tool Holder Shank Width –
Reference Position (7) 495
B.2.8 Number Symbol Identifying Tool Length –
Reference Position (8) 495
B.2.9 Letter Symbol Identifying Indexable Insert Size –
Reference Position (9) 497
Appendix C
Basics of Vector Analysis 499
C.1 Vectors and Scalars .499
C.2 Definition and Representation .500
C.2.1 Definitions 500
C.2.2 Basic Vector Operations 503
C.3 Application Conveniences .509
C.4 Rotation: Linear and Angular Velocities .511
C.4.1 Planar Linear and Angular Velocities 511
C.4.2 Rotation: The Angular Velocity Vector .515
References .518
Appendix D
Hydraulic Losses: Basics and Gundrill Specifics 519
D.1 Hydraulic Pressure Losses – General 519
D.1.1 Major Losses: Friction Factor 520
D.1.2 Minor Losses (Losses Due to Form Resistance) 521xxii Contents
D.2 Concept of the Critical MWF Velocity and Flow Rate .521
D.2.1 MWF Flow Rate Needed for Reliable Chip Transportation .522
D.2.3 Example D.1 .527
D.3 Inlet MWF pressure .528
D.4 Analysis of Hydraulic Resistances 532
D.4.1 Analysis of Hydraulic Resistances Over Which the Designer
Has No or Little Control 532
D.4.2 Variable Resistances Over Which the Designer Has Control 535
D.5 Practical Implementation in the Drill Design 539
References 543
Appendix E
Requirements and Examples of Cutting Tool Drawings 545
E.1 Introduction .545
E.2 Tool Drawings – the Existent Practice 546
E.3 Tool Drawing Requrements 548
E.4 Examples of Tool Drawing .553
References 559
Index…………………………………………………………………………….561
Index
A
Alignment 218, 351, 352, 355−359,
365, 411, 412
Angle of twist 217, 219, 359
Angular velocity 119−124, 288, 314,
327, 376, 513, 515−517
Approach angle 60, 68, 113, 142,
270, 275, 292, 370, 372, 372, 376,
378, 380, 382, 385, 387−389, 392,
393, 407, 428–430, 433, 435−436,
438, 440, 493, 509, 511
Axial force 6, 133, 198, 213,
214,217, 218, 220−225, 229,231,
238, 244, 245, 250, 253, 255,
256,258, 269, 299, 306, 222, 342,
345, 347, 384, 429, 453, 454
Axial force-torque coupling
221−223
B
Backtaper 150, 152−158, 395
Definition 150
Significance 152–158
Basic kinematic scheme of drilling
350−353
Bending moments, gundrill 391−394
Boring 82, 87, 444−449
Bottom clearance space 264−267,
397−399, 415−417, 420−424, 430,
529, 531, 532, 538−540, 542, 543
Definition 397
MWF pressure management 413
Topology 399
Briks criterion 164, 455
Broaches 197−198
Built-up Edge (BUE) 4, 16, 33, 143,
153, 155, 178, 181, 242, 243, 262,
299, 300, 423
C
Chibreakers 179, 250
Chip 3
Silver white 181
Chip compression ratio (CCR) 3, 4,
11, 22, 37−39, 41−46, 132, 146, 165,
169, 175, 176, 182, 183, 188, 249,
261, 427, 455, 456, 459, 460
Chip flow 59, 249, 434
Angle 136, 137, 180, 181, 199,
280
Direction 69, 92, 98, 136, 137,
178, 180, 193−195, 197, 300, 339,
249, 280562 Index
Chip structure 12, 13, 27, 29
Chip thickness 3, 11, 22, 38, 39, 45,
56, 92, 185, 188, 427, 542
Chip velocity 3, 4, 29, 44, 280
Chisel edge 209−213, 220−249, 257,
260, 270, 280, 295−300
Combined point grind 365
Conical point grind 315−321
Coolant holes 260
Location and size 263, 264,
345,536, 549, 551, 553
Cutting 2−49
Free 3, 59
Feed 66, 84, 85, 100, 129, 134,
139, 141−144, 148, 149, 159, 160,
167−169, 185, 218, 219, 229, 287,
325, 326, 375, 376, 380, 427, 428,
434−438, 443, 448, 451, 509
Force 1−9, 9, 23–28, 133−135,
145−147, 164−169, 174, 175, 177,
178, 186, 190, 191, 213−225,
345−350, 453−459
Non-free 55, 59, 60
Orthogonal 25, 42, 57, 58
Oblique 58, 59
Speed 3, 4, 13, 35, 44, 57, 58,
66, 67, 91, 98, 112, 119, 125, 273,
283, 287, 329, 366−369, 371, 379,
448−459
Cutting edge 3, 11, 12, 23, 24,
56−77, 108−117
Major 56, 57, 60, 66, 69, 77, 85,
86, 103, 105−111
Minor Major 56, 57, 60, 66, 69,
77, 85, 86, 103, 105−108
Cutting edge inclination angle 35,
58, 59, 69, 81, 87, 88, 96, 99,
103,107,109, 11, 193−195, 197–201,
249, 280, 281
Cutting edge radius 35, 163−171,
429
Cutting tool selection 74−77
Cutting tool surface and elements 3,
56
Flank face 3, 57
Rake face 3, 57
Shank 57, 359
D
Deep-hole machining operations 343
Gundrill type 343
BTA type 344
Ejector type 344, 345
Deformation mode 2−5
Deformation zone 24, 29, 30, 168
State of stress 30, 183, 454
Depth of cut 56, 60, 129, 135−139,
145, 146, 445, 449−451
Dovetail forming tool 117−119
Drill 206
Basic terms 208−211
Classification 206−208
DIN Classification 223, 224
Point 223
Point angle 63, 150, 209, 270,
278, 288−292, 315
Point geometry 229, 230, 234,
238, 235, 303
With partitioned cutting edge
347−350
With single cutting edge
345−347
Drill-to-diameter ratio (L/D) 341,
342
Drilling force system 213
Drilling system 353−362
Drilling torque, 213−217
E
Edge preparation 160−172
hone radius 163
finish 169
methods 172
Elastic recovery (see also
springback) 83, 151−158, 164,
Energy partition 166, 455−461
F
Feed motion 12, 56−58, 65, 66, 84,
90, 92, 95−97, 102, 186, 314,
444−453
Feed rate 58, 95, 218, 434, 448−451Index 563
Flank angle 3, 68−108, 112−125,
191−193, 278, 281−292, 315−324,
370−390, 407−409, 464, 465
Back 68, 104−107, 370−390
Normal 68, 104−108, 269, 369,
428−429
Optimal 82, 192, 193
Orthogonal 68, 88, 104−108,
117−119, 370−390, 437, 438
Side 68, 104−108, 370−390
Flank face 3, 16, 57, 92−96,
104−107, 160, 167, 191, 264,
270−324, 416, 417
Flute 206−21
Modification 247−254
Profile 208, 245−254
Width ratio 245,246
Fracture 9−18, 22−49
Frequency of chip formation
457−461
Friction force at the tool-workpiece
interface 166
Fundamental laws
First Metal-Cutting Law
(Makarow’s law) 32
Second law of metal cutting (the
deformation law) 35, 36
G
Gundrilling system 354–362
Common issues 356−363
Gundrill geometry 362−439
H
Helix angle 207−210, 222, 227,
275−277
Helical flank face 239, 246, 321−324
Helical point 321−324, 364
Helical rake face 275−279
I
Indexable cutting inserts 74−84
ANSI code 464−471
Geometry parameters 77−84
ISO code 471−491
Inner angle 363, 392
Interference 70, 94−96, 100, 158,
159, 290−292, 398−400, 405
Condition of free penetration
290−292, 398−405
Model 290−292
K
Kinematic angles 92−101
Flank angle 92−101
Inclination angle 99
Rake angle 96, 99
M
Machining regime 448, 449
Mean shear stress at the tool chip
interface 177
Metal cutting, definition 28, 29
Metal working fluid (MWF) 154,
155, 157, 186, 190, 205, 218,
263−267, 342−345, 357−359,
397−399, 413−425, 519−544
Critical velocity 523−526
Critical flow rate 521−526
Flow rate 523, 526−529
Inlet pressure 529−533, 541
Optimal velocity 524−526
Pressure 413−425
Milling tools 198−201
Model of chip formation 3, 4
N
Nose radius 56, 60, 78, 108,
137−146, 457, 468, 470
O
Optimization of tool geometry
439−441
Original coordinate system 271, 272,
292, 365, 366, 370, 375, 385, 386
Outer angle 363, 392
P
Penetration rate 212, 213−223
Constrains 218
Measures to increase 224−259564 Index
Plastic deformation 3−11, 15−22,
35−44, 164−177, 458−460
Point grinds, gundrill 414−418
Poletica criterion 175−176
Power spent on plastic deformation
455, 458−460
Primary motion 57, 58, 66, 68, 90,
97, 443−452
R
Rake angle 3, 56, 68, 70−74, 77, 78,
88, 89, 92−99, 104, 112, 167,
167−169, 172−191, 225−230,
272−279, 332−337
Back 68, 103−108
Effective 183−191
Extremely high 173, 188−190
Neutral 79, 92, 173−178
Negative 79, 173−175
Normal 68, 104−109
Orthogonal 69, 89, 104−109
Side 68, 104−109
Origin of the term 173
Positive 79, 173
References planes 66, 67
Assumed working 66
Cutting edge normal 67
Main reference 66
Orthogonal 67
Tool back 66, 67
Tool cutting edge 66
Relative Tool Sharpness (RTS)
164−167
Resultant cutting motion 58, 91
Rotary tools, turning 195−196
Self-propelled 196
Spinning 195−196
Rule No. 1 in drill design 392
Rule No. 2 in drill design 393
Rule No. 3 in drill design 398,
423−424
Rule No. 4 in drill design 399
S
Self-centering 218, 254−259
Self-piloting drill (SPD) 345–350
Self-piloting tool 345–350
Shear angle 3,4, 20
Shear plane 3,4
Shear strain 11−13, 39, 40
Shoulder dub-off 364, 413−422
Length 417−419
Side passage 413, 414−422
Outlet cross-sectional area
414−422
Auxiliary 423, 424
Single point cutting tool, 56
Single-shear plane model 3, 22−28
Split-point geometry 234−238
Springback (see elastic recovery)
Stagnation zone 417, 418
Static equilibrium 213−216
Straight-flute drill 269−275
Stress-strain diagram 152
String 367−369
Deflector 369
System approach 211−213, 353−362
System consideration 354−362
System objective 212
Systems of consideration of the tool
geometry 61
tool-in-hand (T-hand-S) 61,
64−68, 74
tool-in-machine (T-mach-S) 61,
64, 65, 90
tool-in-use (T-use-S) 61,
90–101
Summation of motions 119−125
Supporting pads 346
T
Tensile test 183–187
elongation 185
neck down 185
frusto-conical section 185
Tool–chip contact length (length of
the tool–chip interface) 175−177,
178−183
elastic part 181, 182
natural 178
plastic part 181, 182
restricted 178−183Index 565
Tool cutting edge angle 66, 73−78,
81−89, 132−150, 270, 276, 298, 315,
216, 330, 334, 335, 465
Tool drawing 545
Critical information 544
Examples 553−558
Existent practice 546−548
Requirements 548−553
Tool failure 351
Tool geometry
selection 129
ideal 130−132
experimental evaluation 132
Influence in edge preparation
167−169
Tool holder 75−83
Geometry parameters 77–83
ISO code 491–487
Tool life 8, 12, 30, 171, 186, 187,
192, 221, 324, 327−330, 191,
427−435
Correlation equation, gundrill
425
Criterion 423
Test 427−435
Tool life, overall 394
Tool minor (end) cutting edge angle
66, 85. 106−108, 146−160
Treading taps 197
Tool wear patterns 395−397
Turning 444−446
U
Ultimate tensile strength 177
Uncut chip cross-sectional area 8,
134, 135
Uncut (undeformed) chip thickness
3, 8,11, 38, 56, 133−141, 146, 159,
167, 168, 175, 325−327
Uncut chip width 56, 136−141, 166
V
Vector 102−125, 499
Definition 500
Analysis 500
Magnitude 500
Unit 502
Resolution into components 502
Vectors 503
Addition 503
Angle between vectors 504
Angle between line and plane
504
Cross-product 506−509
Scalar (dot) product 502
Scalar triple product 509
W
Waterfall edge preparation 163
Wear curves 431
Wear pattern 11, 12
Web 211
Conventional 244
Eccentricity/lip index error 260,
261
Thickness 211, 222, 247
Thickness ratio 246
Thinning 231−233
Wide 244
Wedge angle 68
Back 68
Normal 68
Orthogonal 68
Side 68
Wiper insert 108−110
Work material
Brittle 14
Constitutive model (flow curve)
26, 36, 43
Ductile 14
Properties in cutting and in FEA
25
Workpiece surfaces 56

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