Global optimization of tool path for five-axis flank milling with a cylindrical cutter.

*(English)*Zbl 1354.70019Summary: In this paper, optimum positioning of cylindrical cutter for five-axis flank milling of non-developable ruled surface is addressed from the perspective of surface approximation. Based on the developed. interchangeability principle, global optimization of the five-axis tool path is modeled as approximation of the tool envelope surface to the data points on the design surface following the minimum zone criterion recommended by ANSI and ISO standards for tolerance evaluation. By using the signed point-to-surface distance function, tool path plannings for semi-finish and finish millings are formulated as two constrained optimization problems in a unified framework. Based on the second order Taylor approximation of the distance function, a sequential approximation algorithm along with a hierarchical algorithmic structure is developed for the optimization. Numerical examples are presented to confirm the validity of the proposed approach.

##### MSC:

70E18 | Motion of a rigid body in contact with a solid surface |

49Q10 | Optimization of shapes other than minimal surfaces |

##### Keywords:

five-axis flank milling; tool path optimization; tool axis trajectory surface; surface approximation; distance function; minimax optimization
PDF
BibTeX
Cite

\textit{H. Ding} and \textit{L. Zhu}, Sci. China, Ser. E 52, No. 8, 2449--2459 (2009; Zbl 1354.70019)

Full Text:
DOI

##### References:

[1] | Liu X W. Five-axis NC cylindrical milling of sculptured surfaces. Comput-Aided Des, 1995, 27(12): 887–894 · Zbl 05476180 |

[2] | Bohez E L J, Senadhera S D R, Pole K, et al. A geometric modeling and five-axis machining algorithm for centrifugal impellers. J Manuf Syst, 1997, 16(6): 422–436 |

[3] | Lee J J, Suh S H. Interference-free tool-path planning for flank milling of twisted ruled surfaces. Int J Adv Manuf Tech, 1998, 14(11): 797–805 |

[4] | Rubio W, Lagarrigue P, Dessein G, et al. Calculation of tool paths for a torus mill on free-form surfaces on five-axis machines with detection and elimination of interference. Int J Adv Manuf Tech, 1998, 14(1): 13–20 |

[5] | Redonnet J M, Rubio W, Dessein G. Side milling of ruled surfaces: Optimum positioning of the milling cutter and calculation of interference. Int J Adv Manuf Tech, 1998, 14(7): 459465 |

[6] | Bedi S, Mann S, Menzel C. Flank milling with flat end milling cutters. Comput-Aided Des, 2003, 35(3): 293–300 |

[7] | Menzel C, Bedi S, Mann S. Triple tangent flank milling of ruled surfaces. Comput-Aided Des, 2004, 36(3): 289–296 · Zbl 05861083 |

[8] | Tsay D M, Her M J. Accurate 5-axis machining of twisted ruled surfaces. ASME J Manuf Sci Eng, 2001, 123(4): 731–738 |

[9] | Gong H, Cao L X, Liu J. Improved positioning of cylindrical cutter for flank milling ruled surfaces. Comput-Aided Des, 2005, 37(12): 1205–1213 · Zbl 05861267 |

[10] | Chiou C J. Accurate tool position for five-axis ruled surface machining by swept envelope approach. Comput-Aided Des, 2004, 36(10): 967–974 · Zbl 05861133 |

[11] | Ding Y, Zhu L M, Ding H. Semidefinite programming for Chebyshev fitting of spatial straight line with applications to cutter location planning and tolerance evaluation. Precis Eng, 2007, 31(4): 364–368 |

[12] | Lartigue C, Duc E, Affouard A. Tool path deformation in 5-axis flank milling using envelope surface. Comput-Aided Des, 2003, 35(4): 375–382 · Zbl 05860984 |

[13] | ISO/R 1101. Technical Drawings-Geometrical Tolearncing. Geneva: International Organization for Standardization, 1983 |

[14] | ANSI Standard Y14.5. Dimensioning and Tolerancing. New York: The American Society of Engineers, 1982 |

[15] | Zhu L M, Ding H. A unified approach for least-squares surface fitting. Sci China Ser G-Phys Mech Astron, 2004, 47(Suppl I): 72–78 |

[16] | Nocedal J, Wright S J. Numerical Optimization. New York: Springer-verlag, 1999 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.