Abstract
This paper presents an advanced octree (AO-rep) model and an implicit formula of a generalized cutter model for five-axis milling simulation. First, the main ideal of the AO-rep model is building a hierarchical structure and representing solid volumes. The AO-rep model utilizes an octree to cull unrelated voxels, and generates a small-scale voxel model in grey octants when a cutter intersects these octants. Using a simplified intersection computation between a cube and triangles in E 3, an STL model can be converted into its AO-rep model at a preprocessing stage. Second, the authors formulate an implicit function of a generalized cutter in moving cutter frame, and determine the function in fixed workpiece frame using the theory of a rigid body motion. Finally, the authors make a simulation of machining an impeller. The result shows that the proposed approach has a high performance of time and space.
Similar content being viewed by others
References
Lorensen W E and Cline H E, Marching cubes: A high resolution 3D surface construction alorgithm, ACM Siggraph Computer Graphics, 1987, 21(4): 163–169.
Fleisig R V and Spence A D, Techniques for accelerating B-rep based parallel machining simulation, Computer-Aided Design, 2005, 37(12): 1229–1240.
Wang W P, Solid modeling for optimizing metal removal of three-dimensional NC end milling, Journal of Manufacturing Systems, 1988, 7(1): 57–65.
Tarng Y S and Chang W S, Dynamic NC simulation of milling operations, Computer-Aided Design, 1993, 25(12): 769–775.
Chappel I T, The use of vectors to simulate material removed by numerically controlled milling, Computer-Aided Design, 1983, 15(3): 156–158.
Jerard P B and Drysdale R L, Mehtods for detecting errors in numerically controlled machining of sculptured surfaces, IEEE, Computer Graphics and Applications, 1989, 9(1): 26–39.
Oliver J H and Goodman E D, Direct dimensional NC verification, Computer-Aided Design, 1990, 22(1): 3–9.
Roy U and Xu Y, 3-D object decomposition with extended octree model and its application in geometric simulation of NC machining, Robotics and Computer-Integrated Manufacturing, 1998, 14(4): 317–327.
Roy U and Xu Y, Computation of a geometric model of a machined part from its NC machining programs, Computer-Aided Design, 1999, 31(6): 401–411.
Yau H T and Tsou L S, Efficient NC simulation for multi-axis solid machining with a universal APT cutter, Journay of Computing and Information Science in Engineering, 2009, 9(2): 021001.1–021001.10.
Jang D, Kim K, and Jung J, Voxel-based virtual multi-axis machining, International Journal of Advanced Manufacturing Technology, 2000, 16(10): 709–713.
Kim Y H and Ko S L, Improvement of cutting simulation using the octree method, International Journal of Advanced Manufacturing Technology, 2006, 28(11–18): 1152–1160.
Maeng S R, Baek N, Shin S Y, and Choi B K, A fast NC simulation method for circularly moving tools in the Z-MAP environment, Proceedings of Geometric Modeling and Processing (ed. by Hu S M and Pottmann H), Washington, USA, 2008.
Muller H, Surmann T, Stautner, Albermann F, and Weinert K, Online sculpting and visualization of multi-dexel volumes, Proceedings of the 8th ACM Symposium on Solid Modelling and Applications (ed. by Elber G and Shapiro V), Seattle, Washington, USA, 2003.
Liu S Q, Ong S K, Chen Y P, and Nee A Y C, Real-time, dynamic level-of-detail management for three-axis NC milling simulation, Computer-Aided Design, 2006, 38(4): 378–391.
Mao J, Liu S, and Gao Z, Three-axis NC milling simulation based on adaptive triangular mesh, Computers & Industrial Engineering, 2011, 60(1): 1–6.
Brunet P and Navazo I, Geometric modelling using exact octree representation of polyhedral objects, Proceedings of Eurographics (ed. by Vandoni C E), Nice, France, 1985.
Schroeder W J and Shephard M S, A combined octree/delaunay method for fully automatic 3-D mesh generation, International Journal for Numerical Methods in Engineering, 1990, 29(1): 37–55.
Saona-Vazquez C, Navazo I, and Brunet P, The visibility octree: A data structure for 3D navigation, Computer & Graphics, 1999, 23(5): 635–643.
Samet H, Spatial data structures, Modern Database Systems, the Object Model, Interoperability and Beyond, 1995: 364–385.
Chiou C J and Lee Y S, Swept surface determination for five-axis numberical control machinning, International Journal of Machine Tools & Manufacture, 2002, 42(14): 1497–1507.
Du S, Surmann T, Webber O, and Weinert K, Formulating swept profiles for five-axis tool motions, International Journal of Machine Tools & Manufacture, 2005, 45(7): 849–861.
Kral I H, Numerical Control Programming in APT, Prentice-Hall, New Jersey, 1986.
Shen L and Yuan C, Implicitization using univariate resultants, Journal of Systems Science and Complexity, 2010, 23(4): 804–814.
Li G, Implicitization of partial differential rational parametric equations, Journal of Systems Science and Complexity, 2006, 19(2): 256–265.
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was supported by the National Science and Technology Major Project under Grant No. 2012ZX01029001-002.
This paper was recommended for publication by Guest Editor LI Hongbo.
Rights and permissions
About this article
Cite this article
Wang, H., Guo, R. Improving the simulation efficiency in five-axis milling by using an advanced octree and an implicit formula of a generalized cutter. J Syst Sci Complex 26, 735–756 (2013). https://doi.org/10.1007/s11424-013-3176-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11424-013-3176-0