Abstract
This paper presents a unified view that allows one to consider the global accessibility question in the context of multi-axis machining, as well as globally quantify and resolve it. No constraints are imposed on the possible orientations of the tool during the machining process neither are any inflicted on the shape of the freeform surface. Being global, the presented method augments and complements contemporary multi-axis tool positioning and verification schemes that were developed in recent years for 5-axis machining; schemes that identify and resolve the gouging problem on a point by point basis for each individual point-location along the tool path.
Given, a freeform surface to be machined, the orientation of the tool at each surface location, and a check surface, the outcome of the proposed method is a global dichotomy that provides the regions of the freeform surface that are accessible without gouging into the check surface.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-0-387-35392-0_40
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L. L. Chen and T. C. Woo. Computational Geometry on the Sphere With applications to Automated Machining. Technical Report No. 89–30, Department of Industrial and Operations Engineering, University of Michigan, August 1989.
L. L. Chen, Shuo-Yan Chou, and T. C. Woo. Separating and Intersecting Spherical Polygons: Computing Machinability on Three-, Four-and Five-Axis Numerically Controlled Machines. ACM Transaction on Graphics, Vol. 12, No. 4, pp 305–326, October 1993.
B. K. Choi, J. W. Park and C. S. Jun. Cutter Location Data Optimization in 5-axis Surface Machining. Computer Aided Design, Vol 25, No. 6, pp 377–386, 1993.
M. P. DoCarmo. Differential Geometry of Curves and Surfaces. Prentice-Hall 1976.
G. Elber and E. Cohen. Hidden Curve Removal for Free Form Surfaces. Computer Graphics, Vol 24, No. 4, pp 95–104, Siggraph, August 1990.
G. Elber and E. Cohen. Second Order Surface Analysis Using Hybrid Symbolic and Numeric Operators. Transactions on Graphics, Vol. 12, No. 2, pp 160–178, April 1993.
G. Elber. Accessibility in 5-axis Milling Environment. CAD, Vol 26, No 11, pp 796–802, November 1994.
G. Elber and E. Cohen. Arbitrarily Precise Computation of Gauss Maps and Visibility Sets for Freeform Surfaces. The third ACM/IEEE Symposium on Solid Modeling and Applications, SLC, Utah, pp 271–279, May 1995.
G. Elber and E. Cohen. A Unified Approach to Accessibility in 5-axis Freeform Milling Environments. Center for Intelligent Systems Tech. Report, CIS 9815, Computer Science Department, Technion. http://www.cs.technion.ac.il/Reports.
J. D. Foley et al. Computer Graphics, Principles and Practice, Second Edition. Addison-Wesley Systems Programming Series, Jul. 1990.
Sujit Verma. Simulation of Numerically Controlled Milling machines. Master Thesis, University of Utah, 1995.
C. Hornung, W. Lellek, P. Rehwald, and W. Strasser. An Area-Oriented Analytical Visibility Method for Displaying Parametrically Defined Tensor-Product Surfaces, Computer Aided Geometric Design, Vol. 2, pp 197–205, 1985
R. B. Jerard and R. L. Drysdale Methods for Geometric Modeling, Simulation and Spatial Verification of NC Machining Programs. Proceedings of the Third IFIP Workshop on Geometric Modeling. Rensselaerville, NY, USA, June 1990.
C. G. Jensen and D. C. Anderson. Accurate Tool Placement and Orientation for Finish Surface Machining. Proceedings of the Symposium of Concurrent Engineering. ASME Winter Annual Meeting, 1992.
Yuan-Shin Lee and Tien Chien Chang. 2-Phase Approach to Global Tool Interference Avoidance in 5-axis Machining. Computer Aided Design, Vol 27, No 10, pp 715–729, October 1995.
Yuan-Shin Lee and Tien Chien Chang. Admissible Tool Orientation Control of Gouging Avoidance for 5-axis Complex Surface machining. Machining. Computer Aided Design, Vol 29, No 7, pp 507–521, 1997.
S. Li and R. B. Jerard. 5-axis Machining of Sculptured Surfaces with a Flat End Cutter. Computer Aided Design, Vol 26, No 3, pp 165–178, 1994.
T. Saito and T. Takahashi. NC machining with G-buffer method. Computer Graphics, Vol 25, No. 4, pp 207–216, Siggraph, July 1991.
T. W. Spencer. Scan Line Rendering for 3-axis NC Toolpath Generation, Simulation, and Verification. Technical Report CSE-TR-43–90, Department of Electrical Engineering and Computer Science, University of Michigan, January 1990, U.S.A.
Y. J. Tseng and S. Joshi. Determining Feasible Tool-approach Directions for Machining Bézier Curves and Surfaces. Computer Aided Design, Vol. 23, No. 5, pp 367–378, June 1991.
D. Zhang, A. Bowyer. CSG Set-Theoretical Solid Modeling and NC Machining of Blend Surfaces. The Second Annual ACM Symposium on Computational Geometry, ACM, 1986.
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© 1999 IFIP International Federation for Information Processing
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Elber, G., Cohen, E. (1999). A Unified Approach to Accessibility in 5-axis Freeform Milling Environments. In: Olling, G.J., Choi, B.K., Jerard, R.B. (eds) Machining Impossible Shapes. IFIP — The International Federation for Information Processing, vol 18. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35392-0_39
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DOI: https://doi.org/10.1007/978-0-387-35392-0_39
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