1st Edition

Generation of Surfaces Kinematic Geometry of Surface Machining

By Stephen P. Radzevich Copyright 2014
    740 Pages 263 B/W Illustrations
    by CRC Press

    738 Pages 263 B/W Illustrations
    by CRC Press

    A commonly used practice in industry is the machining of sculptured part surfaces on a multiaxis numerical control (NC) machine. While this practice is vital, it is also a costly aspect of the surface generation process. After investing more than 40 years of research into the theory of part surface generation, the author of Generation of Surfaces: Kinematic Geometry of Surface Machining considers an approach that provides optimal machining while factoring in the lowest possible cost.

    This book presents the modern theory of part surface generation with a focus on kinematic geometry of part surface machining on a multiaxis (NC) machine, and introduces key methods for applying the DG/K-based approach to part surface generation. The DG/K approach is based on the results of research found in two main areas: differential geometry (DG) of surfaces, and kinematics (K) of rigid body in three-dimensional Euclidian space E3. It is an extremely powerful tool for solving a plurality of problems in mechanical/manufacturing engineering.

    The text is presented in three parts: the basics, the fundamentals, and applications of part surface generation. The first part of the book provides an analytical description of part surfaces, details the principal elements of the theory of multiparametric motion of a rigid body in E3 space, and defines applied coordinate systems. The second half introduces the theory of part surface generation, and includes an analytical description of contact geometry, while the final portion illustrates the potential development of highly effective part surface generation methods.

    The author illustrates the most complex features of the book with examples, explains all of the results of analysis mathematically, and uses just one set of input parameters—the design parameters of the part surface to be machined.

    The book considers practical applications for part surface machining and cutting tool design. Developed for use with computer-aided design (CAD) and computer-aided machining (CAM), this text is useful for anyone starting work on new software packages for sculptured part surface machining on a multiaxis NC machine.

    Section I Basics

    Part Surfaces: Geometry

    Elements of Differential Geometry of Surfaces

    On the Difference between Classical Differential Geometry and Engineering Geometry of Surfaces

    On the Classification of Surfaces

    Principal Kinematics of Part Surface Generation

    Kinematics of Sculptured Part Surface Generation

    Generating Motions of the Cutting Tool

    Motions of Orientation of the Cutting Tool

    Relative Motions Causing Sliding of a Surface over Itself

    Possible Kinematic Schemes of Part Surface Generation

    Kinematics of Part Surface Machining Processes

    Axodes and Pitch Surfaces in Generation of Part Surface

    Examples of Implementation of the Principal Kinematic

    Schemes of Part Surface Generation

    Applied Coordinate Systems and Linear Transformations

    Applied Coordinate Systems

    Coordinate System Transformation

    Useful Equations

    Chains of Consequent Linear Transformations and a Closed

    Loop of Consequent Coordinate Systems Transformations

    Impact of the Coordinate Systems Transformations on

    Fundamental Forms of the Surface

    Section II Fundamentals

    Geometry of Contact between a Sculptured Part Surface and

    Generating Surface of the Form-Cutting Tool

    Local Relative Orientation of a Part Surface and of the Cutting Tool

    The First-Order Analysis: Common Tangent Plane

    The Second-Order Analysis: Second Fundamental Form

    The Second-Order Analysis: Planar Characteristic Images

    Degree of Conformity of Two Smooth Regular Surfaces in the First Order of Tangency

    Plücker Conoid: More Characteristic Curves

    Feasible Types of Contact of a Part Surface P and Generating

    Surface T of the Cutting Tool

    Profiling of Form-Cutting Tools of Optimal Design for Machining a Given Part Surface

    Profiling of the Form-Cutting Tools for Sculptured Surface

    Machining

    Generation of Enveloping Surfaces

    Profiling of the Form-Cutting Tools for Machining Parts on

    Conventional Machine Tools

    Characteristic Line E of the Surface P and Generating

    Surface T of the Cutting Tool

    Selection of the Form-Cutting Tools of Rational Design

    Form-Cutting Tools Having Continuously Changeable

    Generating Surface T

    Incorrect Problems in Profiling the Form-Cutting Tools

    Principal Types of Problems in Profiling Form-Cutting Tools

    The Geometry of the Active Part of a Cutting Tool

    Transformation of the Body Bounded by the Generating Surface T into the Cutting Tool

    Geometry of the Active Part of Cutting Tools in the Tool-in-Hand System

    Geometry of the Active Part of Cutting Tools in the Tool-in-Use System

    On the Capabilities of the Analysis of Geometry of the

    Active Part of Cutting Tools

    Conditions of Proper Part Surface Generation

    Optimal Workpiece Orientation on the Worktable of a

    Multiaxis Numerical Control (NC) Machine

    Necessary and Sufficient Conditions of Proper Part Surface Generation

    Global Verification of Satisfaction of the Conditions of

    Proper Part Surface Generation

    Accuracy of Surface Generation

    Two Principal Types of Deviations of the Machined Part

    Surface from the Nominal Part Surface

    Local Approximation of the Contacting Part Surface P and the Generating Surface T of the Form-Cutting Tool

    Calculation of the Elementary Surface Deviations

    Total Displacement of the Cutting Tool with Respect to the Part Surface

    Effective Reduction of the Elementary Surface Deviations

    Principle of Superposition of the Elementary Surface Deviations

    Section III Application

    Selection of the Criterion of Optimization

    Criteria of the Efficiency of Part Surface Machining

    Productivity of Part Surface Machining

    Interpretation of the Part Surface Generation Output as a Function of Conformity

    Synthesis of the Part Surface Machining Operations

    Synthesis of the Most Favorable Part Surface Generation Process: The Local Analysis

    Synthesis of the Most Favorable Part Surface Generation

    Process: The Regional Analysis

    Synthesis of the Most Favorable Part Surface Generation Process: The Global Analysis

    Rational Reparameterization of the Part Surface

    Possibility of the DG/K-based CAD/CAM System for Optimal Sculptured Part Surface Machining

    Major Blocks of the DG/K-based CAD/CAM System

    Examples of Implementation of the DG/K-Based Method of Part Surface Generation

    Machining of Sculptured Part Surfaces on a Multiaxis

    Numerical Control (NC) Machine

    Machining of Surfaces of Revolution

    Finishing of Involute Gears

    Conclusion

    References

    Appendices

    Index

    Biography

    Dr. Stephen P. Radzevich is a professor of mechanical and manufacturing engineering. 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 manufacturing. Dr. Radzevich has spent approximately 40 years developing software, hardware, and other processes for gear design and optimization, developing numerous software packages dealing with CAD and CAM of precise gear finishing. He authored and coauthored over 30 monographs, handbooks, and textbooks, and also authored and coauthored over 250 scientific papers and holds over 220 patents on inventions in the field.

    … the investigation of the problem of synthesizing of the most favorable processes of part surface generating is the main strength of the book by Dr. Radzevich. … It should be stressed here that the problems of synthesizing of something are commonly recognized as the most difficult problems in science, and in engineering in particular."
    ––Dr. Joseph Bukhbinder, Professor (retired), Mechanical Engineering

    "This is a nice systematic approach. … extremely important for scientists and engineers…"
    ––Professor, Dr.Sci., Ph.D. Aleksandr Yurievich Brailov, Odessa Academy of Civil Engineering and Architecture, Ukraine