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**A closed-form solution to the problem of optimal tool-path generation for sculptured surface machining on multi-axis NC machine.**
*(English)*
Zbl 1187.74262

Summary: The topic of the paper is in the field of sculptured surface machining (SSM) on multi-axis NC machines. It presents novel results of investigation of tool-path generation for sculptured surface machining on multi-axis NC machines. The purpose of the paper is to develop an integral form of solution to the problem of optimal tool-path generation. The concept of time-minimal tool-paths is introduced, as well as the optimization problem being formulated analytically. The problem of optimization is subdivided into the following three partial sub-problems: (a) the problem of local tool-path generation; (b) the problem of regional tool-path generation, and finally, (c) the problem of global tool-path generation. The paper presents a closed-form solution to the first two sub-problems. A solution to the problem of optimal tool-path generation is given in the form of an integral equation. The obtained solution enables one to retain the optimal cutter configuration (i.e., the cutter position, and the cutter orientation), as well as the optimal instant direction of feed-rate at every cutter location-point (further, CC-point).

### MSC:

74S99 | Numerical and other methods in solid mechanics |

74P99 | Optimization problems in solid mechanics |

### Keywords:

sculptured surface; local topology; differential vicinity; NC machine; tool-path generation; optimal cutter configuration; cutter location; cutter orientation; CAD/CAM; kinematics of SSM
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\textit{S. P. Radzevich}, Math. Comput. Modelling 43, No. 3--4, 222--243 (2006; Zbl 1187.74262)

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### References:

[1] | Kim, B.H.; Choi, B.K., Guide surface based tool path generation in 3-axis milling: an extension of the guide plane method, Computer-aided design, 32, 3, 191-199, (2000) |

[2] | Choi, B.K.; Jerard, R.B., Sculptured surface machining. theory and applications, (1998), Kluwer Academic Publishers Dordrecht, Boston, London, 368 pages |

[3] | Radzevich, S.P., Fundamentals of surface generation, monograph, (2001), Rastan Kiev, 592 pages (in Russian) |

[4] | Radzevich, S.P., Sculptured surface machining on multi-axis NC machine. monograph, (1991), Vishcha Shkola Publishing House Kiev, 192 pages (in Russian) |

[5] | Radzevich, S.P.; Goodman, E.D., Efficiency of multi-axis NC machining of sculptured part surfaces, (), 42-58 |

[6] | Dragomatz, D.; Mann, S., A classified bibliography of literature on NC milling path generation, Computer-aided design, 29, 3, 239-247, (1997) |

[7] | Marciniak, K., Geometric modeling for numerically controlled machining, (1991), Oxford University Press New York, 245 pages · Zbl 0849.65006 |

[8] | Sarma, R.; Dutta, D., The geometry and generation of NC tool paths, ASME journal of mechanical design, 119, 2, 253-258, (1997) |

[9] | Sarma, R.; Dutta, D., Tool path generation for NC grinding, International journal of machine tool and manufacture, 38, 3, 177-196, (1998) |

[10] | Park, S.C.; Choi, B.K., Tool-path planning for direction-parallel area milling, Computer-aided design, 32, 1, 17-25, (2000) |

[11] | Balasubramaniam, M., Generation of collision-free 5-axis tool paths using a haptic surface, Computer-aided design, 34, 4, 267-279, (2002) |

[12] | Lo, C.-C., Two-stage cutter-path scheduling for ball-end milling of concave and wall-bounded surfaces, Computer-aided design, 32, 10, 597-603, (2000) |

[13] | Lartigue, C., NC tool path in terms of B-spline curves, Computer-aided design, 33, 4, 307-319, (2001) |

[14] | Balasubramaniam, M., Generating 5-axis NC roughing paths directly from a tessellated representation, Computer-aided design, 32, 4, 261-277, (2000) |

[15] | Chiou, C.-J.; Lee, Y.-S., A machining potential field approach to tool path generation for multi-axis sculptured surface machining, Computer-aided design, 34, 5, 357-371, (2002) · Zbl 1383.70003 |

[16] | Kim, T.; Sarma, S.E., Toolpath generation along directions of maximum kinematic performance; a first cut at machine-optimal paths, Computer-aided design, 34, 6, 453-468, (2002) |

[17] | Feng, H.-Y.; Li, H., Constant scallop-height tool path generation for three-axis sculptured surface machining, Computer-aided design, 34, 9, 647-654, (2002) |

[18] | Park, S.C., Tool-path generation for Z-constant contour machining, Computer-aided design, 35, 1, 27-36, (2003) |

[19] | Choi, B.K.; Ko, K., C-space based CAPP algorithm for freeform die-cavity machining, Computer-aided design, 35, 2, 179-189, (2003) |

[20] | Narayanaswami, R.; Pang, J., Multi-resolution analysis as an approach for tool path planning in NC machining, Computer-aided design, 35, 2, 167-178, (2003) |

[21] | Ding, S., Adaptive iso-planar tool path generation for machining of free-form surfaces, Computer-aided design, 35, 2, 141-153, (2003) |

[22] | Yang, D.C.H., Boundary-conformed tool-path generation for trimmed free-form surfaces, Computer-aided design, 35, 2, 127-139, (2003) |

[23] | S.P. Radzevich, A Method of Optimal Work-Piece Orientation on the Worktable of Multi-Axis NC Machine, Pat. No.1442371 (USSR). Filed: February 17, 1987 |

[24] | Radzevich, S.P., \(\mathbb{R}\)-mapping based method for designing of form cutting tool for sculptured surface machining, Mathematical and computer modelling, 36, 7-8, 921-938, (2002) · Zbl 1063.53005 |

[25] | Radzevich, S.P., A cutting-tool-dependent approach for partitioning a sculptured surface, Computer-aided design, 37, 7, 767-778, (2005) |

[26] | Radzevich, S.P.; Goodman, E.D., Computation of optimal workpiece orientation for multi-axis NC machining of sculptured part surfaces, ASME journal of mechanical design, 124, 2, 201-212, (2002) |

[27] | Radzevich, S.P., Conditions of proper sculptured surface machining, Computer-aided design, 34, 10, 727-740, (2002) |

[28] | doCarmo, M.P., Differential geometry of curves and surfaces, (1976), Prentice-Hall New York, 503 pages |

[29] | Piegl, L.; Tiller, W., The NURBS book. (monographs in visual communications), (1995), Springer New York, 646 pages |

[30] | S.P. Radzevich, A Method of Designing a Form Cutting Tool for Sculptured Surface Machining on Multi-Axis NC Machine.-Patent application 4242296/08 (USSR), Filed: 31.03.1987 |

[31] | S.P. Radzevich, A Method of Sculptured Surface Machining on Multi-Axis NC Machine, Pat. No. 1249787, USSR, B23C 3/16, Filed: December 27, 1984 |

[32] | S.P. Radzevich, A Method of Sculptured Surface Machining on Multi-Axis NC Machine, Pat. No. 1185749, USSR, B23C 3/16, Filed: October 24, 1983 |

[33] | Mortenson, M., Geometric modeling, (1985), John Wiley & Sons NY |

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