Abstract
Simulation and verification of numerically controlled (NC) manufacturing processes require efficient visualization and analysis of the swept volume generated by the motion of freeform NC tools along complex 3D paths. State-of-the-art methods are either based on approximation techniques (thus lacking the level of accuracy required in NC manufacturing) or are based on analytical solutions with high computational complexity, which are not suitable for real-time applications. In addition, until recently, modeling the self-intersection of a generated volume was thought to be obstructed by seemingly complex mathematics. This paper proposes solving the sweeping problem by using the sweep-envelope differential equation (SEDE). This method has advantages over other methods in terms of low computational complexity and high accuracy. Moreover, this method includes efficient tools for self-intersection detection and modeling. In this paper, we present an enhanced self-intersection algorithm and apply the SEDE algorithm on a ball-end cutter that is swept along non-intersecting and self-intersecting cutter paths.
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References
Faux ID, Pratt MJ (1979) Computational geometry for design and manufacture. Ellis Horwood-Publishers, Chicester, UK, pp 36–37
Wang WP, Wang KK (1986) Real-time verification of multi-axis NC programs with raster graphics. Proc IEEE Int Conf on Robotics and Automation, pp 364–375
Chung YC, Park JW, Shin H, Choi BK (1998) Modeling the surface swept by a generalized cutter for NC verification. CAD 30(8):587–594
Abdel-Malek K, Yeh HJ (1997) Geometric representation of the swept volume using Jacobian rank-deficiency conditions. CAD 29(6):457–468
Glaeser G, Groller E (1998) Efficient volume-generation during the simulation of NC-Milling. Mathematical visualization. Springer, Berlin Heidelberg New York, pp 89–106
Kim YJ, Varadhan G, Lin MC, Manocha D (2004) Fast swept volume approximation of complex polyhedral models. CAD 36:1013–1027
Yang J, Abdel-Malek K (2005) Approximate swept volumes of NURBS surfaces or solids. Comput Aided Geom Des 22:1–26
Leu MC, Blackmore D, Wang L, Pak K (1995) Implementation of SDE method to represent cutter swept volumes in 5-axis NC milling. Proc Int Conf Intell Manuf, Wuhan, China, pp 111–220
Blackmore D, Leu MC, Wang KK (1992) Applications of flows and envelopes to NC machining. Ann CIRP 41(1):493–496
Blackmore D, Leu MC, Wang L (1997) The sweep-envelope differential equation algorithm and its application to NC machining verification. CAD 29(9):629–637
Wang L (1997) Modeling of 3D swept volumes using SDE/SEDE methods and its application to five-axis NC machining. PhD Dissertation. New Jersey Institute of Technology, Newark, NJ
Wang L (2000) An N2logN algorithm for generating swept solids in NC verification
Irvin KH (1986) Numerical control programming in APT. Englewood Cliffs, Prentice Hall, NJ
Blackmore D, Samulyak R, Leu MC (1999) Trimming swept volumes. CAD 31:215–223
Guigue P, Devillers O (2003) Fast and robust triangle-triangle overlap test using orientation predicates. J Graph Tools 8:25–42
Elden L, Wittmeyer-Koch L (1990) Numerical analysis. Academic Press, San Diego, CA, pp 112
Jiang H (1993) The flow approach to swept volume. MSc Thesis, Dept of Math., New Jersey Institute of Technology, Newark, NJ
Scheidegger CE, Fleishman S, Silva CT (2005) Triangulating point set surfaces with bounded error. In: Desbrun M, Pottmann H (eds) Eurographics Symposium on Geometry Processing
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Podshivalov, L., Fischer, A. Modeling an envelope generated by 3D volumetric NC tool motion. Int J Adv Manuf Technol 38, 949–957 (2008). https://doi.org/10.1007/s00170-007-1148-z
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DOI: https://doi.org/10.1007/s00170-007-1148-z