Advanced Numerical Methods to Optimize Cutting Operations of Five Axis Milling Machines (eBook)

Preface 7
Contents 9
List of Figures 11
List of Tables 16
1 Introduction 17
1.1 Motivation and Structure of the Book 17
1.2 CAD/CAM Formats 19
1.3 Short Literature Survey 20
References 32
2 Introduction to Five-Axis NC Machining 41
2.1 Five-Axis NC Machining Concepts 41
2.2 NC Part Programming 44
2.3 Classification of Five-Axis Machines 50
2.4 Five-Axis Machine Kinematics 53
2.5 Five-Axis Machining Example 59
References 64
3 Fundamental Issues in Tool Path Planning 67
3.1 Surface Representation 67
3.2 Machining Strip Width Estimation 69
3.3 Optimal Tool Orientation and Gouging Avoidance 76
3.4 Kinematics Error 79
3.5 Tool Path Generation 82
References 84
4 Space-Filling Curve Tool Paths 89
4.1 History of Space-Filling Curves and Their Applications 89
4.2 Tool Path Optimization 91
4.3 Tool Path Generation using Adaptive Space-filling Curves 93
4.4 Examples and Discussion 99
References 110
5 Tool Paths in Adaptive Curvilinear Coordinates 113
5.1 Introduction 113
5.2 A Historical Note on Grid Generation 114
5.3 Variational Grid Generation for Tool Path Optimization 117
5.4 Application of Harmonic Functional to Tool Path Generation 132
5.5 Space-Filling Curve Generation on Block Structured Grid 140
5.6 Examples and Discussion 141
Appendix: Derivation of Computational Formulas for Adaptive- Harmonic Grid Generation 149
References 160
6 Optimization of Rotations 167
6.1 Introduction 167
6.2 Kinematics Error and Angle Variation 171
6.3 Optimization Problem 176
6.4 Optimization Problems: Examples and Practical Machining 178
6.5 Uniform Angular Grids 184
6.6 Uniform Angular Grids: Numerical and Machining Experiments 192
Appendix: The APT cutter 198
References 199
7 Theory of Optimal Setup for Five-Axis NC Machining 201
7.1 Introduction 201
7.2 Tool Trajectory Analysis 205
7.3 Least-Squares Optimization and Dependent Variables 208
7.4 Examples and Discussion 210
References 218
Index 221