Table Of ContentGear Cutting Tools
Science and Engineering
Second Edition
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Gear Cutting Tools
Science and Engineering
Second Edition
Stephen P. Radzevich
CRC Press
Taylor & Francis Group
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Library of Congress Cataloging‑in‑Publication Data
Names: Radzevich, S. P. (Stepan Pavlovich), author.
Title: Gear cutting tools : science and engineering / Stephen P. Radzevich.
Description: Second edition. | Boca Raton : Taylor & Francis, CRC Press, 2018. | Includes bibliographical references and index.
Identifiers: LCCN 2017010753| ISBN 9781138037069 (hardback) | ISBN 9781315178042 (ebook)
Subjects: LCSH: Gear-cutting machines. | Gearing--Design and construction. | Metal-cutting tools--Design and construction--
Mathematical models. | Machinery, Kinematics of--Mathematical models.
Classification: LCC TJ187 .R34 2018 | DDC 621.9/44--dc23
LC record available at https://lccn.loc.gov/2017010753
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Contents
Preface .....................................................................................................................................................................................xvii
Acknowledgments ..................................................................................................................................................................xix
Author .......................................................................................................................................................................................xxi
Introduction ..........................................................................................................................................................................xxiii
Syntax .....................................................................................................................................................................................xxix
1. Brief Notes on the History of Methods of Machining Gears and of Design of Gear Cutting Tools ...............1
1.1 Early Accomplishments in the Design of Toothed Wheels and in Methods for Manufacture of Gears ...2
1.2 Early Designs of Special-Purpose Cutting Tools for Producing Gear Teeth ...................................................3
1.3 Gear Cutting Tools for the First Production Machines ......................................................................................4
1.4 Evolution of Gear Cutting Tools for Production Machines ..............................................................................5
1.5 Development of the Skiving Internal Gear Process ............................................................................................7
1.6 Development of the Rotary Gear Shaving Process .............................................................................................7
1.7 Grinding Hardened Gears ......................................................................................................................................8
1.8 Gear Cutting Tools for Generating Bevel Gears ..................................................................................................8
1.9 Later Accomplishments in Design of Gear Cutting Tools for Generating Bevel Gears ................................9
1.10 Generating Milling of Bevel Gears ......................................................................................................................12
Section I Basics
2. Gears: Geometry of Tooth Flanks ................................................................................................................................17
2.1 Basic Types of Gears ..............................................................................................................................................17
2.2 Analytical Description of Gear Tooth Flanks ....................................................................................................18
2.2.1 Tooth Flank of a Spur Involute Gear ......................................................................................................21
2.2.2 Tooth Flank of a Helical Involute Gear ..................................................................................................21
2.2.3 Tooth Flank of a Straight Bevel Gear .....................................................................................................24
2.2.4 Tooth Flank of a Skew Bevel Gear ..........................................................................................................24
2.3 Gear Tooth Surfaces That Allow for Sliding over Them ..................................................................................25
3. Principal Kinematics of Gear Machining Process ....................................................................................................27
3.1 Relative Motions in Gear Machining Process ....................................................................................................27
3.1.1 Elementary Relative Motions of the Work Gear and the Gear Cutting Tool ...................................27
3.1.2 Feasible Relative Motions of the Work Gear and the Gear Cutting Tool ..........................................29
3.2 Rolling of Conjugate Surfaces ..............................................................................................................................30
4. Kinematics of Continuous Indexing Methods of Gear Machining Processes ...................................................31
4.1 Vector Representation of Gear Machining Process ...........................................................................................31
4.2 Kinematic Relationships for Gear Machining Mesh ........................................................................................36
4.3 Configuration of Vectors of Relative Motions ....................................................................................................39
4.3.1 Principal Features of Configuration of Two Rotation Vectors ............................................................39
4.3.2 Classification of Gear Machining Meshes .............................................................................................41
4.4 Kinematics of Gear Machining Processes ..........................................................................................................43
Section II Form Gear Cutting Tools
5. Gear Broaching Tools .....................................................................................................................................................47
5.1 Kinematics of Gear Broaching Process ...............................................................................................................47
5.2 Generating Surface of a Gear Broach ..................................................................................................................47
vii
viii Contents
5.3 Cutting Edges of Gear Broaching Tools ..............................................................................................................48
5.3.1 Rake Surface of Finishing Teeth of Gear Broach .................................................................................49
5.3.1.1 Conical Rake Surface ..............................................................................................................49
5.3.1.2 Rake Surface in the Form of Screw Archimedean Surface ...............................................50
5.3.2 Clearance Surface of Gear Broach Teeth ...............................................................................................50
5.4 Chip Removal Diagrams .......................................................................................................................................51
5.5 Sharpening of Gear Broaches ...............................................................................................................................52
5.6 Novel Concept of Precision Gear Broaching Tool for Machining Helical Involute Gears ..........................57
5.7 Application of Gear Broaching Tools ..................................................................................................................59
5.7.1 Broaching Internal Gears ........................................................................................................................59
5.7.2 Broaching External Gears .......................................................................................................................61
5.8 Shear-Speed Cutting ..............................................................................................................................................62
5.8.1 Principle of Shear-Speed Cutting of Gears ...........................................................................................62
5.8.2 Profiling of Form Tools for Shear-Speed Cutting of Gears ................................................................63
5.8.2.1 Descriptive Geometry-Based Method for Profiling of Form Tools .................................63
5.8.2.2 Analytical Profiling of the Form Tool ..................................................................................64
5.8.3 Application of Shear-Speed Cutting ......................................................................................................66
5.9 Rotary Broaches: Slater Tools ...............................................................................................................................66
5.10 Broaching Bevel Gear Teeth .................................................................................................................................68
5.10.1 Principle of Revacycle Process of Cutting Gear Teeth ........................................................................68
5.10.2 Revacycle Cutting Tools ..........................................................................................................................70
5.10.3 Profiling Cutter for Machining Straight Bevel Gears by Using Revacycle Process .......................71
5.10.3.1 Profiling the Finishing Teeth of Revacycle Gear Cutter ....................................................71
5.10.3.2 Shape of Roughing Teeth of Revacycle Gear Cutter ..........................................................74
5.10.4 Application of Revacycle Process of Cutting Gear Teeth ...................................................................75
6. End Mill Gear Cutters ....................................................................................................................................................77
6.1 Kinematics of Gear Cutting with End Mill Cutter ............................................................................................77
6.2 Generating Surface of End Mill Gear Cutter ......................................................................................................77
6.2.1 Equation for Generating Surface of End Mill Cutter for Machining Spur Involute Gears ...........78
6.2.2 Equation for Generating Surface of End Mill Cutter for Machining Helical Involute Gears .......80
6.2.3 Elements of Intrinsic Geometry of Generating Surface of End Mill Gear Cutter...........................83
6.3 Cutting Edge of End Mill Gear Cutter ................................................................................................................83
6.3.1 Rake Surface of Mill Cutter for Machining Involute Gears ...............................................................84
6.3.1.1 Rake Surface in a Form of Plane ...........................................................................................84
6.3.1.2 Rake Surface in the Form of Screw Archimedean Surface ...............................................85
6.3.2 Clearance Surface of Mill Cutter for Machining Involute Gears ......................................................86
6.3.3 Cutting Edge Geometry of End Mill Gear Cutter ...............................................................................88
6.3.3.1 Rake Surface Is a Plane ..........................................................................................................89
6.3.3.2 Rake Surface Is a Screw Surface ...........................................................................................91
6.4 Accuracy of Gear Tooth Flanks Machined by End Mill Cutters .....................................................................93
6.4.1 Background of Approach ........................................................................................................................93
6.4.2 Cusps on Tooth Flanks of Spur Gear ....................................................................................................93
6.4.3 Cusps on Tooth Flanks of Helical Gear ................................................................................................94
6.4.3.1 Normal Curvature of Helical Gear Tooth Flank in Direction of Feed Motion F ..........95
c
6.4.3.2 Calculation of Deviation of Machined Tooth Flank of Helical Gear
from Its Desired Shape ...........................................................................................................95
6.5 Application of End Mill Gear Cutters .................................................................................................................96
7. Disk Mill Gear Cutters ...................................................................................................................................................99
7.1 Kinematics of Gear Cutting by Disk Mill Cutter ...............................................................................................99
7.2 Generating Surface of Disk Mill Gear Cutter...................................................................................................100
7.2.1 Equation for Generating Surface of Disk Mill Gear Cutter for Machining Spur Involute Gear ......100
7.2.2 Equation for Generating Surface of Disk Mill Cutter for Machining Helical Involute Gears .....102
7.2.3 Elements of Intrinsic Geometry of the Generating Surface of Disk Mill Gear Cutter ..................103
Contents ix
7.3 Cutting Edge of Disk Mill Gear Cutter .............................................................................................................105
7.3.1 Rake Surface of Disk Mill Gear Cutter for Machining Involute Gears ...........................................105
7.3.2 Clearance Surface of Disk Mill Gear Cutter for Machining Involute Gear ....................................106
7.4 Profiling of Disk Mill Gear Cutters ...................................................................................................................107
7.4.1 Use of Descriptive Geometry-Based Method of Profiling ................................................................107
7.4.2 Analytical Profiling of Disk Mill Gear Cutters ..................................................................................109
7.4.2.1 Important Intermediate Conclusion .....................................................................................112
7.5 Cutting Edge Geometry of Disk Mill Gear Cutter ...........................................................................................113
7.6 Disk Mill Cutters for Roughing of Gears ..........................................................................................................116
7.7 Accuracy of Gear Tooth Flanks Machined by Disk Mill Gear Cutters .........................................................119
7.8 Application of Disk Mill Gear Cutters ..............................................................................................................121
8. Nontraditional Methods of Gear Machining by Form Cutting Tools ................................................................129
8.1 Plurality of Single Parametric Motions .............................................................................................................129
8.2 Implementation of Single Parametric Motions for Designing Form Gear Cutting Tool ...........................130
8.2.1 End Mill Gear Cutter ..............................................................................................................................131
8.2.2 Disk Mill Gear Cutter .............................................................................................................................131
8.2.3 Face Mill Gear Cutter .............................................................................................................................132
8.2.4 Enveloping Round Broach for Cutting Spur and Helical Gears ......................................................133
8.2.5 Enveloping Round Broach for Machining Straight Bevel Gears .....................................................134
8.3 Diversity of Form Tools for Machining a Given Gear ....................................................................................135
8.3.1 Machining of Worm on Lathe ...............................................................................................................135
8.3.2 Milling of Involute Worm ......................................................................................................................137
8.3.3 Thread Whirling .....................................................................................................................................139
8.3.4 Grinding of Involute Worm ...................................................................................................................140
8.4 On Classification of Form Gear Cutting Tools .................................................................................................142
Section III Cutting Tools for Continuous Indexing Methods of Generating
Gear Teeth: Parallel-Axes Gear Machining Mesh
9. Rack Cutters for Planing of Spur and Helical Gears .............................................................................................145
9.1 Generating Surface of Rack Cutter ....................................................................................................................145
9.1.1 Equation for Generating Surface of Rack Cutter ................................................................................145
9.2 On the Variety of Feasible Tooth Profiles of Rack Cutters .............................................................................148
9.3 Cutting Edge of Rack Cutter ...............................................................................................................................150
9.3.1 Rake Surface of Rack Cutter ..................................................................................................................150
9.3.1.1 Rake Plane Is Perpendicular to Generating Straight Lines of Surface T .........................150
9.3.1.2 Rake Plane Is at the Helix Angle to Generating Straight Lines of Surface T .................151
9.3.2 Clearance Surface of Rack Cutter Tooth ..............................................................................................151
9.4 Profiling of Rack Cutter Teeth ............................................................................................................................152
9.4.1 Profiling of Rack Cutter Teeth by Using DG-Based Methods ..........................................................152
9.4.2 Analytical Profiling of Rack Cutter Teeth ...........................................................................................153
9.5 Cutting Edge Geometry of Rack Cutter ............................................................................................................154
9.5.1 Calculation of Cutting Tool Geometry for Lateral Cutting Edges ...................................................154
9.5.2 Possible Improvements in the Geometry of Lateral Cutting Edges of Rack Cutters ....................156
9.5.2.1 Modifications of Rake Surface ...............................................................................................156
9.5.2.2 Modifications of Clearance Surface ......................................................................................158
9.6 Chip Thickness Cut by Cutting Edges of Rack Cutter Tooth ........................................................................159
9.7 Accuracy of Planed Gear ....................................................................................................................................163
9.7.1 Fulfillment of the Fifth Condition of Proper Part Surface Generation .........................................163
9.7.2 Fulfillment of the Sixth Condition of Proper Part Surface Generation ........................................165
9.8 Application of Rack Cutters .................................................................................................................................167
9.9 Potential Improvements in Methods of Gear Cutting and Designs of Rack Gear Cutters ........................167
