3rd Edition
Generation of Surfaces Kinematic Geometry of Surface Machining
Preface
Introduction
Author
Acknowledgements
Part I. Basics
1. Part Surfaces: Geometry
1.1. Elements of Differential Geometry of Surfaces
1.2. On the Difference between Classical Differential Geometry and Engineering Geometry of Surfaces
1.3. Classification of Surfaces: Local Surface Patches
2. Principal Kinematics of Part Surface Generation
2.1. Kinematics of Sculptured Part Surface Generation
2.2. Generating Movements of the Cutting Tool
2.3. Movements of Orientation of the Cutting Tool: Their Types and Classification
2.4. Relative Movements that Result in Sliding of Surface on Itself: Their Types and Classification
2.5. Kinematic Schemes of Part Surface Generation: Possible Types and Classification
2.6. Kinematics of Part Surface Machining Processes
2.7. Axodes and Pitch Surfaces in the Theory of Part Surface Generation
2.8. Examples of the Use of Principal Kinematic Schemes of Part Surface Generation
3. Applied Coordinate Systems and Linear Transformations
3.1. Applied Coordinate Systems
3.2. Coordinate System Transformation
3.3. Useful Equations
3.4. Chains of Successive Linear Transformations and a Closed Cycle of Successive Coordinate Systems
3.5. The influence of Coordinate Systems Transformations on Fundamental Forms at a Surface Point
Part II Fundamentals
4. Geometry of Contact between a Sculptured Part Surface and Generating Surface of the Form Cutting Tool
4.1. Local Relative Orientation of the Part Surface and of the Cutting Tool
4.2. First-Order Analysis: Common Tangent Plane
4.3. Second-Order Analysis: The Second Fundamental Form
4.4. Second-Order Analysis: Planar Characteristic Images
4.5. Degree of Conformity of Two Smooth Regular Surfaces in the First-Order of Tangency
4.6. Plücker Conoid: More Characteristic Curves
4.7. Types of Contact of the Part Surface, , and the Generating Surface, , of the Cutting Tool
5. Profiling of Form Cutting Tools of Optimal Design for Machining a Given Part Surface
5.1. Profiling of Form Cutting Tools for Sculptured Surface Machining
5.2. Generation of Envelope Surfaces
5.3. Profiling of Form Cutting Tools for Machining Part Surfaces on Conventional Machine Tools: On Machine Tools with Non-Agile Kinematics of Machining
5.4. Characteristic Line, , of the Part Surface, , and the Generating Surface, T, of the Cutting Tool
5.5. Selection of Form Cutting Tools of Rational Design
5.6. Form Cutting Tool with Continuously Variable Generating Surface
5.7. Incorrect Problems in Profiling of Form Cutting Tools
5.8. Principal Problems in Profiling of Form Cutting Tools
6. Geometry of the Active Part of the Cutting Tool
6.1. Transformation of a Body Bounded by a Generating Surface, , into a Cutting Tool
6.2. Geometry of the Active Part of Cutting Tools in the Tool-in-Hand System
6.3. Geometry of the Active Part of Cutting Tools in the Tool-in-Use System
6.4. Potential Possibilities of Analyzing of the Geometry of the Active Part of Cutting Tools
7. Conditions of Proper Part Surface Generation
7.2. Necessary and Sufficient Conditions for the Proper Part Surface Generation
7.3. Global Verification of Fulfillment of the Necessary Conditions for Proper Part Surface Generation
8. Accuracy of Surface Generation..
8.1. Two Principal Types of Deviations of the Machined Part Surface from the Nominal Part Surface
8.1.1. Principal deviations of the first kind
8.1.2. Principal deviations of the second kind
8.1.3. Resulting deviation of the machined part surface
8.2. Local Approximation of the Part Surface, , and the Generating Surface, , of the Form Cutting Tool in Contact
8.3. Calculation of Elementary Surface Deviations
8.4. Total Displacement of the Cutting Tool Relative to the Surface of the Part..
8.5. Effective Reduction of Elementary Surface Deviations
8.6. On the Admissibility of Applying the Principle of Superposition of Elementary Surface Deviations
Part III Application
9. Selecting an Optimization Criterion
9.1. Criteria for the Efficiency of Part Surface Machining
9.2. Productivity of Part Surface Machining
9.3. Interpretation of the Rate of Part Surface Generation as a Function of Conformity
10. Synthesis of Advantageous Operations for Part Surface Machining
10.1. Synthesis of the Most Advantageous Process for Forming the Surface of a Part: Local Analysis
10.2. Synthesis of the Most Advantageous Process for Forming the Surface of a Part: Regional Analysis
10.3. Synthesis of the Most Advantageous Process for Forming the Surface of a Part: Global Analysis
10.4. Rational Re-parameterization of the Part Surface
10.5. On the Possibility of Using a DG/K-Based CAD/CAM System for Optimal Machining of Sculptured Part Surface
10.6. Potential Architecture of a DG/K-based CAD/CAM System
11. Examples of Using the DG/K-Based Method of Generating Part Surfaces
11.1. Machining of Sculptured Part Surfaces on a Multi-Axis Numerical Control (NC) Machine
11.3. Finishing of Involute Gears
Conclusion
Notation
References
Bibliography
Appendices
Appendix A: Elements of Differential Geometry of Surfaces
Appendix B: Elements of Vector Calculus
Appendix C: Changing Surface Parameters
Appendix D: Non-Cartesian Reference Systems
Appendix E: Elements of Spherical Trigonometry
Biography
Stephen P. Radzevich is a Professor of Mechanical Engineering, and a Professor of Manufacturing Engineering at Kyiv Polytechnic Institute in Ukraine. He received his M.Sc. in 1976, Ph.D. in 1982, and Dr.(Eng)Sc. in 1991, all in mechanical engineering. Dr. Radzevich has extensive industrial experience in gear design and gear manufacture, and has developed numerous software packages dealing with computer-aided design (CAD) and computer-aided machining (CAM) of precise gear finishing for a variety of industrial sponsors. His main research interest is the field of Kinematics and Geometry of Gearing, particularly with a focus on precision gear design, high-power-density gear trains, torque share in split-power-transmission systems (SPTS), design of special purpose gear cutting/finishing tools, and design and machine (finish) of precision gears for low-noise and noiseless transmissions of automotives. Amongst his book publications are Advances in Gear and Design Manufacture (2019), Dudley's Handbook of Practical Gear Design and Manufacture, Fourth Edition (2021), and Theory of Gearing, Fourth Edition (2026).
