Korean Journal of Computational Design and Engineering (한국CDE학회논문집)

Society for Computational Design and Engineering (한국CDE학회)
권호 표지

A Z-map Update Method for Linearly Moving tools

직선 운동하는 공구에 대한 Z-맵의 갱신 방법

  • Published : 2002.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

In numerically controlled(NC) machining simulation, a Z-map has been used frequently for representing a workpiece. Since the Z-map is usually represented by a set of Z-axis aligned vectors, the machining process can be simulated through calculating the intersection points between the vectors and the surface swept by a machining tool. In this paper, we present an efficient method to calculate those intersection points when an APT-type tool moves along a linear tool path. Each of the intersection points can be expressed as the solution of a system of non-linear equations. We transform this system of equations into a single-variable equation, and calculate the candidate interval in which the unique solution exists. We prove the existence of a solution and its uniqueness in this candidate interval. Based on these characteristics, we can effectively apply numerical methods to finally calculate the solution of the non-linear equations within a given precision. The whole process of NC simulation can be achieved by updating the Z-map properly. Our method can provide more accurate results with a little more processing time, in comparison with the previous closed-form solution.

Keywords

References

  1. IEEE Computer Graphics and Applications v.6 no.12 Geometric Modeling for Swept Volume of Moving Solids Wang, W. P.;Wang, K. K. https://doi.org/10.1109/MCG.1986.276586
  2. SIGGRAPH'86 Proceedings v.20 no.4 Real-time Shaded NC Milling Display Van Hook, T. https://doi.org/10.1145/15886.15887
  3. The Visual Computer v.5 Approximate Methods for Simulation and Verification of Numerically Controlled Machining Programs Jerard, R. B.;Hussaini, S. Z.;Drysdale, R. L.;Schaudt, B. https://doi.org/10.1007/BF01999101
  4. Journal of Manufacturing Systems v.14 no.5 Integrated Simulation, Error Assessment, and Tool Path Correction for Five-Axis NC Milling Huang, Y.;Oliver, J. H. https://doi.org/10.1016/0278-6125(95)98870-C
  5. Computer-Aided Design v.25 no.4 Realtime 3D Simulation of 3-axis Milling using Isometric Projection Hsu, P. L.;Yang, W. T. https://doi.org/10.1016/0010-4485(93)90052-P
  6. Proceedings of the Third Pacific Conference on Computer Graphics and Applications, Pacific Graphics '95 Application and Extension of Z-map Model Choi, B. K.;Chung, Y. C.;Park, J. W.
  7. Computer-Aided Design v.30 no.8 Modeling the Surfaces Swept by a Generalized Cutter for NC Verification Chung, Y. C.;Park, J. W.;Shin, H. Y.;Choi, B. K. https://doi.org/10.1016/S0010-4485(97)00033-X
  8. Technical Report TR-521-96 Application Challenges to Computational Geometry CG Impact Task Force Report
  9. Journal of Mechanical Design v.114 Efficient Intersection of Surface Normals with Tool Swept Volmumes for Discrete Three-axis NC Verification Oliver, J. H. https://doi.org/10.1115/1.2916944
  10. Proceedings of ASME Advances in Design Automation v.2 Intersection of Rays with Parametric Envelope Surfaces Representing Five-axis NC Milling Tool Swept Volumes Ashish, P. Narvekar;Yunching Huang;James H. Oliver;D. A. Hoeltzel(ed.)
  11. Differential Geometry of Curves and Surfaces Manfredo, P. Do Carmo
  12. Numerical Recipes in C Press, W. H.;Teukolsky, S. A.;Vetterling, W. T.;Flannery, B. P.
  13. The C++Programming Language Stroustrup, B.
  14. The Inventor Mentor Wernecke, J.