Generation of Surfaces: Kinematic Geometry of Surface Machining, 1st Edition (Paperback) book cover

Generation of Surfaces

Kinematic Geometry of Surface Machining, 1st Edition

By Stephen P. Radzevich

CRC Press

738 pages | 263 B/W Illus.

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Description

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.

Reviews

… 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

Table of Contents

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

About the Author

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.

Subject Categories

BISAC Subject Codes/Headings:
SCI041000
SCIENCE / Mechanics / General
TEC009070
TECHNOLOGY & ENGINEERING / Mechanical
TEC016000
TECHNOLOGY & ENGINEERING / Industrial Design / General