## Advanced Numerical Methods to Optimize Cutting Operations of Five Axis Milling MachinesThis book presents new optimization algorithms designed to improve the efficiency of tool paths for five-axis NC machining of sculptured surfaces. The book covers both the structure of the SLAM problem in general and proposes a new extremely efficient approach. It can be used by undergraduate and graduate students and researchers in the field of NC machining and CAD/CAM as well as by corporate research groups for advanced optimization of cutting operations. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Introduction | 1 |

12 CADCAM Formats | 3 |

13 Short Literature Survey | 4 |

References | 16 |

Introduction to FiveAxis NC Machining | 25 |

22 NC Part Programming | 28 |

23 Classification of FiveAxis Machines | 34 |

24 FiveAxis Machine Kinematics | 37 |

532 Variational Method and Functionals | 102 |

533 The Harmonic Functional | 109 |

534 Examples of the Tool Path Optimization | 110 |

54 Application of Harmonic Functional to Tool Path Generation | 116 |

55 SpaceFilling Curve Generation on Block Structured Grid | 124 |

56 Examples and Discussion | 125 |

Derivation of Computational Formulas for AdaptiveHarmonic Grid Generation | 133 |

References | 144 |

25 FiveAxis Machining Example | 43 |

References | 48 |

Fundamental Issues in Tool Path Planning | 50 |

32 Machining Strip Width Estimation | 53 |

33 Optimal Tool Orientation and Gouging Avoidance | 60 |

34 Kinematics Error | 63 |

35 Tool Path Generation | 66 |

References | 68 |

SpaceFilling Curve Tool Paths | 73 |

42 Tool Path Optimization | 75 |

43 Tool Path Generation using Adaptive Spacefilling Curves | 77 |

432 SpaceFilling Curve Generation | 78 |

433 Tool Path Correction | 80 |

44 Examples and Discussion | 83 |

References | 94 |

Tool Paths in Adaptive Curvilinear Coordinates | 96 |

52 A Historical Note on Grid Generation | 98 |

53 Variational Grid Generation for Tool Path Optimization | 101 |

Optimization of Rotations | 151 |

62 Kinematics Error and Angle Variation | 155 |

63 Optimization Problem | 160 |

Examples and Practical Machining | 162 |

65 Uniform Angular Grids | 168 |

Numerical and Machining Experiments | 176 |

The APT cutter | 182 |

183 | |

Theory of Optimal Setup for FiveAxis NC Machining | 184 |

72 Tool Trajectory Analysis | 189 |

722 Workpiece Setup and the Tool Trajectory | 190 |

73 LeastSquares Optimization and Dependent Variables | 192 |

732 Dependent Variables | 193 |

74 Examples and Discussion | 194 |

742 Examples | 195 |

202 | |

204 | |

### Other editions - View all

### Common terms and phrases

2-0 machine adaptive grid algorithm angular grid applicable axis Bohez CC points Computational Computer-Aided Design conﬁguration constraints constructed corresponding curvature curvilinear grid deﬁned diﬀerence eﬀective cutting eﬃcient equations feedrate ﬁrst Five-axis ﬁve-axis machining ﬂat-end cutter function G-code geometric given gouging avoidance Hamiltonian path International Journal interpolation isoparametric tool paths iterations kinematics error linear machine coordinates machine slide Machine Tools machined surface machining strip width Makhanov mapping Mathematics method milling machine minimization NC machining node NURBS oﬀset optimal setup Optimization with regard parameters parametric surface plane principal curvatures problem radius reﬁnement rotary axes rotation angles S2 on MAHO scallop height sculptured surface SFC tool path shown in Fig simulation solid modeling space-ﬁlling curve speciﬁc stationary point structured grid surface in Example surface machining surface normal tool orientation tool path optimization tool path planning tool tip Unassigned vector Voronoi diagrams word address workpiece coordinate system