Kinematic Geometry of Surface Machining  book cover
1st Edition

Kinematic Geometry of Surface Machining

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ISBN 9781420063400
Published December 14, 2007 by CRC Press
536 Pages 212 B/W Illustrations

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Book Description

The principle of Occam’s razor loosely translates to “the simplest solution is often the best”. The author of Kinematic Geometry of Surface Machining utilizes this reductionist philosophy to provide a solution to the highly inefficient process of machining sculptured parts on multi-axis NC machines. He has developed a method to quickly calculate the necessary parameters, greatly reduce trial and error, and achieve efficient machining processes by using less input information, and in turn saving a great deal of time.

This unique method will allow youto calculate optimal values for all major parameters of sculptured surface machining on multi-axis NC machines.It is much faster than conventional methods because it requires only minimal input information for the development of extremely efficient machining operations. Radzevich simply utilizes the geometric information of a particular part surface to be machined for developing optimal surface machining process rather than wasting time dealing with unnecessary data.

This one-of-a-kind resource guides you through this cutting-edge technique beginning with an analytical description of part surfaces, the basics of differential geometry for sculptured surfaces, and the principal elements of the multi-parametric motion on a rigid body in E3 space theory. The book reveals the analytical method for investigating cutting tool geometry and explains a set of described conditions required for proper part surface generation. Next, the author illustrates the selection of criterion for optimization and describes the synthesis of optimal machining operations. He includes examples of the DG/K based method of surface generation implementation.

Written by a leading expert in the field who holds over 150 patents, Kinematic Geometry of Surface Machining invokes Occam’s well-known philosophical principle so that you can apply the simplest solution to achieve optimal, time-saving surface machining processes.

Table of Contents

Part I: Basics
Part Surfaces: Geometry
Elements of differential geometry of surfaces
On difference between classical differential geometry and engineering geometry
On classification of surfaces
Kinematics of Surface Generation
Kinematics of sculptured surface generation
Generating motions of the cutting tool
Motions of orientation of the cutting tool
Relative motions those causing sliding of a surface over itself
Feasible kinematic schemes of surface generation
On a possibility of the replacement of axodes with pitch surfaces
Examples of implementation of the kinematic schemes of 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 surfaces
Part II: Fundamentals
The Geometry of Contact of Two Smooth Regular Surfaces
Local relative orientation of a part surface and of the cutting tool
The first order analysis: common tangent plane
The second order analysis
Rate of conformity of two smooth regular surfaces in the first order of tangency
Plücker’s conoid: more characteristic curves
Feasible kinds of contact of the surfaces p and t
Profiling Of the Form Cutting Tools of the Optimal Design
Profiling of the form cutting tools for sculptured surface machining
Generating of enveloping surfaces
Profiling of the form cutting tools for machining parts on conventional machine tools
Characteristic line  of the part surface  and of the generation surface  of the cutting tool
Selection of the form cutting tools of rational design
The form cutting tools having continuously changeable the generating surface
Incorrect problems in profiling of the form cutting tools
Intermediate conclusion
Geometry of 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 capabilities of the analysis of geometry of the active part of cutting tools
Conditions of Proper Part Surface Generation
Optimal work-piece orientation on the worktable of multi-axis 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 kinds of deviations of the machined surface from
    the nominal part surface
Local approximation of the contacting surfaces P and T
Computation 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 elementary surface deviations
Part III: Application
Selection of the Criterion of Optimization
Criteria of the efficiency of part surfaces machining
Productivity of surface machining
Interpretation of the surface generation output as a function of   conformity
Synthesis of Optimal Surface Machining Operations
Synthesis of optimal surface generation: the local analysis
Synthesis of optimal surface generation: the regional analysis
Synthesis of optimal surface generation: the global analysis
Rational re-parameterization of the part surface
On a possibility of the DG/K-based CAD/CAM system for optimal sculptured surface machining
Examples of Implementation of the Dg/K-Based Method of Surface Generation
Machining of sculptured surfaces on multi-axis NC machine
Machining of surfaces of revolution
Finishing of involute gears

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