Leu, M.C.; Blackmore, D.; Wang, L.P.; Pak, K.G.
Implementation of SDE method to represent cutter swept volumes in 5-axis NC milling
Author(s): Leu, M.C.; Blackmore, D.; Wang, L.P.; Pak, K.G.
Corporate Source: New Jersey Inst. of Technology, Newark, NJ, USA
Source: Proceedings of SPIE - The International Society for Optical Engineering Int. Conference on Intelligent Manufacturing Jun 10 1995 v
2620 1995 Wuhan, China Sponsored by: SPIE - Int Soc for Opt Engineering, Bellingham, WA USA Society of Photo-Optical Instrumentation
Engineers Bellingham WA USA p 354-364 ISSN: 0277-786X CODEN: PSISDG ISBN: 0-8194-2012-3 Publication Year: 1995
Abstract: The sweep differential equation (SDE) method is based upon analyzing and computing the boundary of the cutter swept volume in 5-axis NC milling. The points on the boundary of the cutter swept volume are shown to be a subset of the union of (1) the grazing points of the cutter for the entire sweep, (2) the ingress points of the cutter at the beginning of the sweep, and (3) the egress points of the cutter at the end of the sweep. The grazing points at each time instant are computed from a tangency function which describes the relationship between the sweep vector and the outward surface normals for all the points on the boundary of the cutter. An algorithm is developed and a software program is written for the computation and display of the tool swept volumes for a typical 5-axis NC milling machine. An example is given to demonstrate the algorithm
in computing the swept volume of a ball-end cutter. In English 18 Refs. EI Order Number: 95092841634
Subjects: Milling machines; Numerical control systems; Differential equations; Cutting tools; Algorithms; Vectors; Computer software; Artificial
intelligence; Computer integrated manufacturing
Identifiers: Cutter swept volumes; Grazing points; 5-axis NC milling machines
Sweep-envelope differential equation algorithm and its application to NC machining verification
Author(s): Blackmore, D.; Leu, M.C.; Wang, L.P.
Corporate Source: New Jersey Inst of Technology, Newark, NJ, USA
Source: Computer Aided Design v 29 n 9 Sep 1997 Elsevier Science Ltd Oxford Engl p 629-637 ISSN: 0010-4485 CODEN: CAIDA5 Publication Year: 1997
Abstract: A new method, called the sweep-envelope differential equation, for characterizing swept volume boundaries is introduced. This method is used as the theoretical foundation of an algorithm for computing swept volumes using the trajectories of the sweep-envelope differential equation which start at the initial grazing points of the moving object. The major advantages of this algorithm are: (1) the grazing point set need
essentially only be computed at the initial position of the object - the remaining grazing points are generated by the flow of the sweep-envelope equation - so the computation complexity is drastically reduced; and (2) it provides automatic connectivity for computed boundary points that facilitates integration with standard algorithms and CAD software for visual realization and Boolean operations. Examples are presented that
illustrate successful integration of a prototype program (based on the algorithm) with commercial NC verification software. In English (Author abstract) 15 Refs. EI Order Number: 97103863478
Subjects: Computer aided design; Differential equations; Algorithms; Computational methods; Boundary conditions; Numerical control systems; Machining; Computer software; Boolean algebra; Computational complexity Identifiers: Sweep envelope differential equation; Swept volume boundaries; Numerically controlled machining
Analysis and modelling of deformed swept volumes
Author(s): Blackmore, Denis; Leu, Ming C.; Shih, Frank
Corporate Source: New Jersey Inst of Technology, Newark, NJ, USA
Source: Computer Aided Design v 26 n 4 Apr 1994 p 315-326 ISSN: 0010-4485 CODEN: CAIDA5 Publication Year: 1994
Abstract: The sweep differential equation approach and the boundary-flow method developed for the analysis and representation of swept volumes are extended to include objects experiencing deformation. It is found that the theoretical framework can be generalized quite naturally to deformed swept volumes by the enlargement of the Lie group structure of the sweeps. All the usual results, including the boundary-flow formula, are shown to have extensions for swept volumes with deformation. Several special classes of deformation are identified, and their particular properties are studied insofar as they pertain to swept volumes. A program for obtaining deformed swept volumes of planar polygons is described, and is then applied to several examples to demonstrate its effectiveness. In English (Author abstract) 24 Refs. EI Order Number: 94121501234
Subjects: Differential equations; Deformation; Mathematical models; Geometry; Manufacture; Computer aided design; Thermal stress; Machining; Strain gages; Thermal effects; Computer software; Boundary layer flow; Algebra Identifiers: Deformed swept volumes; Sweep differential equations; Similarity deformations; Linear deformations; Nonlinear deformations; Boundary flow formula; Lie groups; Manufacturing design; Numerically controlled machining verification; Planar polygons