كتاب Kinematic Geometry of Surface Machining
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 كتاب Kinematic Geometry of Surface Machining

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مُساهمةموضوع: كتاب Kinematic Geometry of Surface Machining   السبت 14 أبريل 2012, 3:03 pm

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Kinematic Geometry of Surface Machining

ويتناول الموضوعات الأتية :

I Basics
Part Surfaces: Geometry
Elements of Differential Geometry of Surfaces
On the Difference between Classical Differential
Geometry
and Engineering Geometry
On the Classification of Surfaces
Surfaces That Allow Sliding over Themselves
Sculptured Surfaces
Circular Diagrams
On Classification of Sculptured Surfaces
References
Kinematics of Surface Generation
Kinematics of Sculptured Surface Generation
Establishment of a Local Reference System
Elementary Relative Motions
Generating Motions of the Cutting Tool
Motions of Orientation of the Cutting Tool
Relative Motions Causing Sliding of a Surface over
Itself
Feasible Kinematic Schemes of Surface Generation
On the Possibility of Replacement of Axodes with Pitch
Surfaces
Examples of Implementation of the Kinematic Schemes
of Surface Generation
References
Applied Coordinate Systems and Linear Transformations
Applied Coordinate Systems
Coordinate Systems of a Part Being Machined
Coordinate System of Multi-Axis Numerical Control
(NC) Machine
Coordinate System Transformation
Introduction
Homogenous Coordinate Vectors
Homogenous Coordinate Transformation
Matrices of the Dimension ×
Translations
by Taylor
& Francis Group, LLC
viii Contents
Rotation about a Coordinate Axis
Rotation about an Arbitrary Axis through the Origin
Eulerian Transformation
Rotation about an Arbitrary Axis Not through the
Origin
Resultant Coordinate System Transformation
An Example of Nonorthogonal Linear Transformation
Conversion of the Coordinate System Orientation
Useful Equations
RPY-Transformation
Rotation Operator
A Combined Linear Transformation
Chains of Consequent Linear Transformations and a
Closed
Loop of Consequent Coordinate System Transformations
Impact of the Coordinate System Transformations on
Fundamental Forms of the Surface
References
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
Preliminary Remarks: Dupin’s
Indicatrix
Surface of Normal Relative Curvature
Dupin’s Indicatrix of Surface of Relative Curvature
Matrix Representation of Equation of the Dupin’s
Indicatrix of the Surface of Relative Normal Curvature
Surface of Relative Normal Radii of Curvature
Normalized Relative Normal Curvature
Curvature Indicatrix
Introduction of the Ir k(P/T) Characteristic Curve
Rate of Conformity of Two Smooth, Regular Surfaces
in the First Order of Tangency
Preliminary Remarks
Indicatrix of Conformity of the Surfaces P and
Directions of the Extremum Rate of Conformity
of the Surfaces P
and T
Asymptotes of the Indicatrix of Conformity CnfR
(P/T)
Comparison of Capabilities of the Indicatrix of
Conformity CnfR (P/T)
and of Dupin’s
Indicatrix of the
Surface of Relative Curvature
Important Properties of the Indicatrix
of Conformity CnfR (P/T)
The Converse Indicatrix of Conformity of the
Surfaces
P and
T in the First Order of Tangency
by Taylor
& Francis Group, LLC
Contents ix
Plücker’s Conoid: More Characteristic Curves
Plücker’s Conoid
Basics
Analytical Representation
Local Properties
Auxiliary Formulas
Analytical Description of Local Topology of the
Smooth, Regular Surface P
Preliminary Remarks
Plücker’s Conoid
Plücker’s Curvature Indicatrix
AnR (P)-Indicatrix
of the Surface P
Relative Characteristic Curves
On a Possibility of Implementation of
Two of Plücker’s Conoids
AnR(P/T)-Relative Indicatrix of the Surfaces
P and
Feasible Kinds of Contact of the Surfaces P and
On a Possibility of Implementation of the Indicatrix
of Conformity for Identification of Kind of Contact of the
Surfaces P
and T
Impact of Accuracy of the Computations on the
Desired
Parameters of the Indicatrices of Conformity CnfR(P/T)
Classification of Kinds of Contact of the Surfaces P and
References
Profiling of the Form-Cutting Tools of the Optimal Design
Profiling of the Form-Cutting Tools for Sculptured
Surface Machining
Preliminary Remarks
On the Concept of Profiling the Optimal
Form-Cutting Tool
R-Mapping of the Part Surface P on
the Generating
Surface T
of the Form-Cutting Tool
Reconstruction of the Generating Surface T of
the Form-Cutting Tool from the Precomputed Natural
Parameterization
A Method for the Determination of the Rate
of Conformity Functions F , F , and F
An Algorithm for the Computation of the Design
Parameters of the Form-Cutting Tool
Illustrative Examples of the Computation of the
Design Parameters of the Form-Cutting Tool
Generation of Enveloping Surfaces
Elements of Theory of Envelopes
by Taylor
& Francis Group, LLC
Contents
Envelope to a Planar Curve
Envelope to a One-Parametric Family of Surfaces
Envelope to a Two-Parametric Family of Surfaces
Kinematical Method for the Determining
of Enveloping Surfaces
Profiling of the Form-Cutting Tools for Machining
Parts
on Conventional Machine Tools
Two Fundamental Principles by Theodore Olivier
Profiling of the Form-Cutting Tools for
Single-Parametric
Kinematic Schemes of Surface Generation
Profiling of the Form-Cutting Tools for
Two-Parametric
Kinematic Schemes of Surface Generation
Profiling of the Form-Cutting Tools for
Multiparametric
Kinematic Schemes of Surface Generation
Characteristic Line E of
the Part Surface P and of the Generating
Surface T
of the Cutting Tool
Selection of the Form-Cutting Tools of Rational Design
The Form-Cutting Tools Having a Continuously
Changeable Generating Surface
Incorrect Problems in Profiling the Form-Cutting Tools
Intermediate Conclusion
References
The Geometry of the Active Part of a Cutting Tool
Transformation of the Body Bounded by the Generating
Surface
T into
the Cutting Tool
The First Method for the Transformation of the
Generating Body of the Cutting Tool into the
Workable Edge Cutting Tool
The Second Method for the Transformation of the
Generating Body of the Cutting Tool into the
Workable Edge Cutting Tool
The Third Method for the Transformation of the
Generating Body of the Cutting Tool into the
Workable Edge Cutting Tool
Geometry of the Active Part of Cutting Tools in the
Tool-in-Hand System
Tool-in-Hand Reference System
Major Reference Planes: Geometry of the Active Part
of a
Cutting Tool Defined in a Series of Reference Planes
Major Geometric Parameters of the Cutting Edge
of a Cutting Tool
Main Reference Plane
Assumed Reference Plane
Tool Cutting Edge Plane
Tool Back Plane
by Taylor
& Francis Group, LLC
Contents xi
Orthogonal Plane
Cutting Edge Normal Plane
Analytical Representation of the Geometric
Parameters
of the Cutting Edge of a Cutting Tool
Correspondence between Geometric Parameters of
the Active Part of Cutting Tools That Are Measured in
Different Reference Planes
Diagrams of Variation of the Geometry of the Active
Part of a Cutting Tool
Geometry of the Active Part of Cutting Tools in the
Tool-in-Use System
The Resultant Speed of Relative Motion in the
Cutting
of Materials
Tool-in-Use Reference System
Reference Planes
The Plane of Cut Is Tangential to the Surface
of Cut at the Point of Interest M
The Normal Reference Plane
The Major Section Plane
Correspondence between the Geometric
Parameters Measured in Different
Reference Planes
The Main Reference Plane
The Reference Plane of Chip Flow
A Descriptive-Geometry-Based Method for the
Determination of the Chip-Flow Rake Angle
On Capabilities of the Analysis of Geometry of the
Active
Part of Cutting Tools
Elements of Geometry of Active Part of a Skiving Hob
Elements of Geometry of the Active Part of a Cutting
Tool
for Machining Modified Gear Teeth
Elements of Geometry of the Active Part of a
Precision Involute Hob
An Auxiliary Parameter R
The Angle fr between
the Lateral Cutting Edges
of the Hob Tooth
The Angle x of Intersection of the Rake Surface
and of the Hob Axis of Rotation
References
Conditions of Proper Part Surface Generation
Optimal Workpiece Orientation on theWorktable
of a Multi-Axis Numerical Control (NC) Machine
Analysis of a GivenWorkpiece Orientation
Gaussian Maps of a Sculptured Surface P and
of the
Generating Surface T of
the Cutting Tool
by Taylor
& Francis Group, LLC
xii Contents
The Area-Weighted Mean Normal to a
Sculptured Surface P
OptimalWorkpiece Orientation
Expanded Gaussian Map of the Generating Surface
of the Cutting Tool
Important Peculiarities of Gaussian Maps
of the Surfaces P
and T
Spherical Indicatrix of Machinability
of a Sculptured Surface
Necessary and Sufficient Conditions of Proper
Part Surface Generation
The First Condition of Proper Part Surface
Generation
The Second Condition of Proper Part Surface Generation

The Third Condition of Proper Part Surface
Generation
The Fourth Condition of Proper Part Surface
Generation
The Fifth Condition of Proper Part Surface
Generation
The Sixth Condition of Proper Part Surface
Generation
Global Verification of Satisfaction of the Conditions
of Proper Part Surface Generation
Implementation of the Focal Surfaces
Focal Surfaces
Cutting Tool (CT)-Dependent Characteristic
Surfaces
Boundary Curves of the CT-Dependent
Characteristic Surfaces
Cases of Local-Extremal Tangency of the Surfaces
P and
T
Implementation of R-Surfaces
Local Consideration
Global Interpretation of the Results
of the Local Analysis
Characteristic Surfaces of the Second Kind
Selection of the Form-Cutting Tool of Optimal Design

Local KLR-Mapping
of the Surfaces P and T

The Global KGR-Mapping of the Surfaces P and
T
Implementation of the Global KGR-Mapping
Selection of an Optimal Cutting Tool
for Sculptured Surface Machining
References
Accuracy of Surface Generation
Two Principal Kinds of Deviations of the Machined
Surface
from the Nominal Part Surface
Principal Deviations of the First Kind
Principal Deviations of the Second Kind
The Resultant Deviation of the Machined Part Surface

by Taylor
& Francis Group, LLC
Contents xiii
Local Approximation of the Contacting Surfaces P and
T
Local Approximation of the Surfaces P and
T
by Portions of Torus Surfaces
Local Configuration of the Approximating Torus
Surfaces
Computation of the Elementary Surface Deviations
Waviness of the Machined Part Surface
Elementary Deviation hss
of the Machined Surface
An Alternative Approach for the Computation
of the Elementary Surface Deviations
Total Displacement of the Cutting Tool with Respect
to the Part Surface
Actual Configuration of the Cutting Tool
with Respect to the Part Surface
The Closest Distance of Approach between
the Surfaces P
and T
Effective Reduction of the Elementary Surface
Deviations
Method of Gradient
Optimal Feed-Rate and Side-Step Ratio
Principle of Superposition of Elementary Surface
Deviations
References
Part
III Application
Selection of the Criterion of Optimization
Criteria of the Efficiency of Part Surface Machining
Productivity of Surface Machining
Major Parameters of Surface Machining Operation
Productivity of Material Removal
Equation of theWorkpiece Surface
Mean Chip-Removal Output
Instantaneous Chip-Removal Output
Surface Generation Output
Limit Parameters of the Cutting Tool Motion
Computation of the Limit Feed-Rate Shift
Computation of the Limit Side-Step Shift
Maximal Instantaneous Productivity of Surface
Generation
Interpretation of the Surface Generation Output
as a Function of Conformity
References
Synthesis of Optimal Surface Machining Operations
Synthesis of Optimal Surface Generation: The Local
Analysis
Local Synthesis
Indefiniteness
by Taylor
& Francis Group, LLC
xiv Contents
A Possibility of Alternative Optimal Configurations
of the Cutting Tool
Cases ofMultiple Points of Contact of the Surfaces P and
T
Synthesis of Optimal Surface Generation: The Regional
Analysis
Synthesis of Optimal Surface Generation: The Global
Analysis
Minimization of Partial Interference
of the Neighboring Tool-Paths
Solution to the Boundary Problem
Optimal Location of the Starting Point
Rational Reparameterization of the Part Surface
Transformation of Parameters
Transformation of Parameters in Connection
with the Surface Boundary Contour
On a Possibility of the Differential
Geometry/Kinematics
(DG/K)-Based Computer-Aided Design/Computer-Aided
Manufacturing (CAD/CAM) System for Optimal Sculptured
Surface Machining
Major Blocks of the DG/K-Based
CAD/CAM System
Representation of the Input Data
OptimalWorkpiece Configuration
Optimal Design of the Form-Cutting Tool
Optimal Tool-Paths for Sculptured Surface Machining
Optimal Location of the Starting Point
References
Examples of Implementation of the Differential Geometry/
Kinematics (DG/K)-Based Method of Surface Generation
Machining of Sculptured Surfaces on a Multi-Axis
Numerical
Control (NC) Machine
Machining of Surfaces of Revolution
Turning Operations
Milling Operations
Machining of Cylinder Surfaces
Reinforcement of Surfaces of Revolution
Finishing of Involute Gears
References
Conclusion
Notation

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كتاب Kinematic Geometry of Surface Machining

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