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Despite decades of extensive research in this field, no solution to the problem of optimal part surface generation has been found. Kinematic Geometry Surface Machining fills the gap between the capabilities of modern multi-axis numerical controlled machines and the demands of the market. This book presents the latest research in the field of optimal surface generation. It provides an overview of modern CAD/CAM systems for high precision sculptured part surfaces. Including real-world examples and end-of-chapter references, the text also explains in detail how to develop the most cost-effective methods of machining for high quality sculptured surfaces on a multi-axis numerical controlled machine.

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 E_{3} 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.

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

Elements of differential geometry of surfaces

On difference between classical differential geometry and engineering geometry

On classification of surfaces

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

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

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

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

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

Transformation of the body bounded by the generating surface

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

Optimal work-piece orientation on the worktable of multi-axis

Necessary and sufficient conditions of proper part surface generation

Global verification of satisfaction of the conditions of proper part surface generation

Two principal kinds of deviations of the machined surface from

the nominal part surface

Local approximation of the contacting surfaces

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

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 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

Machining of sculptured surfaces on multi-axis

Machining of surfaces of revolution

Finishing of involute gears

ISBN: **9781420063400**

Condizione: Nuovo

Dimensioni: 9.25 x 6.125 in Ø 1.90 lb

Formato: Copertina rigida

Illustration Notes:212 b/w images, 1 table and 684 equations

Pagine Arabe: 536

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