Geometry of Surfaces A Practical Guide for Mechanical Engineers

This updated and expanded edition presents a highly accurate specification for part surface machining. Precise specification reduces the cost of this widely used industrial operation as accurately specified and machined part surfaces do not need to undergo costly final finishing. Dr. Radzevich describes techniques in this volume based primarily on classical differential geometry of surfaces. He then transitions from differential geometry of surfaces to engineering geometry of surfaces, and examines how part surfaces are either machined themselves, or are produced by tools with surfaces that are precisely machined. The book goes on to explain specific methods, such as derivation of planar characteristic curves based on Plücker conoid constructed at a point of the part surface, and that analytical description of part surface is vital for surfaces machined using CNC technology, and especially so for multi-axes NC machines. Providing readers with a powerful tool for analytical description of part surfaces machined on conventional machine tools and numerically controlled machines, this book maximizes understanding on optimal treatment of part surfaces to meet the requirements of today’s high tech industry.

Part 1. Part Surfaces.- Geometry of a Part Surface.- On a Possibility of Classification of Part Surfaces.- Part 2. On a Possibility of Classification of Part Surfaces.- Early Works in the Field of Contact Geometry of Surfaces.- An Analytical Method based on Second Fundamental Forms of the Contacting Part Surfaces.- Indicatrix of Conformity at Point of Contact of Two Smooth Regular Part Surfaces in the First Order of Tangency.- Plücker Conoid: More Characteristic Curves.- Possible Kinds of Contact of Two Smooth Regular Part Surfaces in the First Order of Tangency.- Part 3. Mapping of Contacting Part Surfaces.- R-Mapping of Interacting Part Surfaces.- Generation of Enveloping Surfaces: General Consideration.- Generation of Enveloping Surfaces: Special Cases.- Conclusion.- Appendix A: Elements of Vector Calculus.- Appendix B: Elements of Coordinate Systems Transformations.- Appendix C: Change of Surface Parameters.- Appendix D: Closest Distance of Approach between Two Part Surfaces.

Dr. Stephen P. Radzevich is a Professor of Mechanical Engineering, and a Professor of Manufacturing Engineering.  He received the M.Sc. (1976), the Ph.D. (1982), and the Dr.(Eng)Sc. (1991) – all in mechanical engineering.  Dr. Radzevich has extensive industrial experience in gear design and manufacture. He has developed numerous software packages dealing with CAD and CAM of precise gear finishing for a variety of industrial sponsors.  His main research interest is Kinematic Geometry of Surface Generation, particularly with the focus on (a) precision gear design, (b) high power density gear trains, (c) torque share in multi-flow gear trains, (d) design of special purpose gear cutting/finishing tools, (e) design and machining (finishing) of precision gears for low-noise/noiseless transmissions of cars, light trucks etc. Dr. Radzevich has spent about 40 years developing software, hardware and other processes for gear design an optimization. Besides his work for industry, he trains engineering students at universities and gear engineers in companies.  He authored and co-authored over 30 monographs, handbooks, and textbooks. The monographs entitled “Generation of Surfaces” (2001), “Kinematic Geometry of Surface Machining” (CRC Press, 2008), “CAD/CAM of Sculptured Surfaces on Multi-Axis NC Machine: The DG/K-Based Approach” (M&C Publishers, 2008), “Gear Cutting Tools: Fundamentals of Design and Computation” (CRC Press, 2010, 2^nd edition 2017), “Precision Gear Shaving” (Nova Science Publishers, 2010), “Dudley’s Handbook of Practical Gear Design and Manufacture” (CRC Press, 2012, 2^nd edition 2016), “Theory of Gearing: Kinematics, Geometry, and Synthesis” (CRC Press, 2012, 2^nd edition 2018), “Geometry of Surfaces: A Practical Guide for Mechanical Engineers” (2013) are among the recently published volumes.  He also authored and co-authored about 350 scientific papers and holds over 250 patents on inventions in the field, both, USA patents and International.