Generation of Surfaces

Generation of Surfaces: Kinematic Geometry of Surface Machining, Third Edition, addresses the critical challenge of optimizing sculptured part surface machining on multi-axis numerical control (NC) machines while minimizing costs. Drawing from over 40 years of research into part surface generation theory, the new edition includes additional information on part surface geometry, expanded appendices, and updated illustrations and formulas presented in a more complete form. This book presents the modern theory of part surface generation with a focus on the kinematic geometry of part surface machining on a multi-axis (NC) machine, and it introduces key methods for applying the DG/K-based approach to part surface generation. Content progresses systematically through three essential parts: basics, fundamentals, and applications of part surface generation. All analytical results are explained mathematically, using a single set of input parameters - the design parameters of the part surface to be machined. Practical applications encompass part surface machining optimization and cutting tool design, with extensive examples illustrating the most complex theoretical concepts, while the methodology integrates seamlessly with computer-aided design (CAD) and computer-aided manufacturing (CAM) systems, making it immediately applicable to industrial practice. The rigorous mathematical foundation combined with practical applications makes this an indispensable reference for advancing multi-axis machining capabilities. This book is essential for mechanical engineers, manufacturing engineers, CAD/CAM software developers, and researchers who are actively involved in the development, implementation, and optimization of multi-axis NC machining systems. It is particularly valuable for professionals engaged in creating innovative software packages for sculptured part surface machining, as well as for individuals aiming to enhance surface generation processes while simultaneously minimizing manufacturing costs and improving overall efficiency.

Stephen P. Radzevich is a Professor of Mechanical Engineering and a Professor of Manufacturing Engineering at Kyiv Polytechnic Institute in Ukraine. He earned an MSc in 1976, a PhD in 1982, and a Dr(Eng)Sc in 1991, all in mechanical engineering. Dr. Radzevich has extensive industrial experience in gear design and gear manufacture, and he has developed numerous software packages dealing with computer-aided design (CAD) and computer-aided manufacturing (CAM) of precise gear finishing for a variety of industrial sponsors. His main research interest is in 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, design of special purpose gear cutting/finishing tools, and design and machine (finishing) of precision gears for low-noise and noiseless automotive transmissions. Among his publications are Advances in Gear and Design Manufacture (2019), Dudley's Handbook of Practical Gear Design and Manufacture, 4th ed. (2021), and Theory of Gearing, 4th ed. (2026).

Part I: Basics. 1. Part Surfaces: Geometry. 2. Principal Kinematics of Part Surface Generation. Part II: Fundamentals. 3. Applied Coordinate Systems and Linear Transformations. 4. Geometry of Contact between the Sculptured Part Surface and the Generating Surface of the Form Cutting Tool. 5. Profiling of Form Cutting Tools of Optimal Design for Machining a Given Part Surface. 6. Geometry of the Active Part of the Cutting Tool. 7. Conditions of Proper Part Surface Generation. 8. Accuracy of Surface Generation. Part III: Application. 9. Selecting an Optimization Criterion. 10. Synthesis of Advantageous Operations for Part Surface Machining. 11. Examples of Using the DG/K-Based Method of Generating Part Surfaces.