MATHSM: medial axis transform toward high speed machining of pockets

Abstract The pocketing operation is a fundamental procedure in NC machining. Typical pocketing schemes compute uniform successive offsets or parallel cuts of the outline of the pocket, resulting in a toolpath with C 1 discontinuities. These discontinuities render the toolpath quite impractical in the context of high speed machining (HSM). This work addresses and fully resolves the need for a C 1 continuous toolpath in HSM and offers MATHSM, a C 1 continuous toolpath for arbitrary C 1 continuous pockets. MATHSM automatically generates a C 1 continuous toolpath that consists of primarily circular arcs while maximizing the radii of the generated arcs and, therefore, minimizing the exerted radial acceleration. MATHSM is especially suited for machining of elongated narrow pockets.

[1]  Farhad Arbab,et al.  An algorithm for generating NC tool paths for arbitrarily shaped pockets with islands , 1992, TOGS.

[2]  R. Farouki,et al.  Voronoi diagram and medial axis algorithm for planar domains with curved boundaries — II: Detailed algorithm description , 1999 .

[3]  D. Ross Computer-aided design , 1961, CACM.

[4]  Martin Held Computing Voronoi Diagrams of Line Segments Reliably and Efficiently , 2000, CCCG.

[5]  Esther M. Arkin,et al.  Optimization Problems Related to Zigzag Pocket Machining , 1996, SODA '96.

[6]  Martin Held,et al.  VRONI: An engineering approach to the reliable and efficient computation of Voronoi diagrams of points and line segments , 2001, Comput. Geom..

[7]  Byoung Kyu Choi,et al.  Die-cavity pocketing via cutting simulation , 1997, Comput. Aided Des..

[8]  Kai Tang,et al.  Traversing the machining graph of a pocket , 2003, Comput. Aided Des..

[9]  Gershon Elber Trimming Local and Global Self-intersections in Offset Curves Using Distance Maps , 2003, IMA Conference on the Mathematics of Surfaces.

[10]  Kai Tang,et al.  An algorithm for reducing tool retractions in zigzag pocket machining , 1998, Comput. Aided Des..

[11]  B. Gurumoorthy,et al.  Constructing medial axis transform of planar domains with curved boundaries , 2003, Comput. Aided Des..

[12]  Martin Held,et al.  A geometry-based investigation of the tool path generation for zigzag pocket machining , 1991, The Visual Computer.

[13]  Young Joon Ahn,et al.  G1 arc spline approximation of quadratic Bézier curves , 1998, Comput. Aided Des..

[14]  大野 義夫,et al.  Computer Graphics : Principles and Practice, 2nd edition, J.D. Foley, A.van Dam, S.K. Feiner, J.F. Hughes, Addison-Wesley, 1990 , 1991 .

[15]  Gershon Elber,et al.  Comparing Offset Curve Approximation Methods , 1997, IEEE Computer Graphics and Applications.

[16]  H. Persson,et al.  NC machining of arbitrarily shaped pockets , 1978 .

[17]  Dharmaraj Veeramani,et al.  Selection of an optimal set of cutting-tool sizes for 2D pocket machining , 1997, Comput. Aided Des..

[18]  James D. Foley,et al.  Fundamentals of interactive computer graphics , 1982 .

[19]  Gábor Lukács,et al.  Pocket machining based on contour-parallel tool paths generated by means of proximity maps , 1994, Comput. Aided Des..

[20]  Eungki Lee,et al.  Contour offset approach to spiral toolpath generation with constant scallop height , 2003, Comput. Aided Des..

[21]  Gershon Elber,et al.  Trimming local and global self-intersections in offset curves/surfaces using distance maps , 2006, Comput. Aided Des..

[22]  S. Y. Wong,et al.  An optimization approach for biarc curve-fitting of B-spline curves , 1996, Comput. Aided Des..

[23]  R. Farouki,et al.  Voronoi diagram and medial axis algorithm for planar domains with curved boundaries I. Theoretical foundations , 1999 .