Skip to main content
SpringerLink
Log in

Discrete simulation of NC machining

  • Published:
Algorithmica Aims and scope Submit manuscript

Abstract

We describe a method for simulating and verifying the correctness of Numerical Control (NC) programs. NC programs contain the sequence of cutting tool movements which machine raw stock into a finished object. Our method is based on a discrete approximation of the object by a set of points. A vector is passed through each of the points and machining is simulated by finding the intersections of tool movements with these vectors. We present a point-selection method and an analysis that shows that the error introduced by the approximation can be made as small as desired. The run time is inversely proportional to the allowable error and the size of the cutting tool, and directly proportional to the distance that the cutting tool moves.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. T. Armstrong, G. C. Carey, and A. dePennington, Numerical Code Generation from a Geometric Modeling System, inSolid Modeling by Computers: From Theory to Applications, M. S. Pickett and J. W. Boyse, eds., Plenum, New York, 1984.

    Google Scholar 

  2. P. Atherton, C. Earl, and C. Fred, A Graphical Simulation System for Dynamic 5-Axis NC Verification, Autofact Show of the Society of Manufacturing Engineers, Detroit, November 1987, 2-1–2-12.

  3. R. O. Anderson, Detecting and Eliminating Collisions in NC Machining,Computer-Aided Design,10(4) (1978), 231–237.

    Article  Google Scholar 

  4. G. T. Armstrong, A Study of Automatic Generation of Non-Invasive Machine Paths from Geometric Models, Ph.D. Dissertation, University of Leeds, October 1982.

  5. P. Bézier,Numerical Control—Mathematics and Applications, Wiley, London, 1972.

    MATH  Google Scholar 

  6. W. Böhm, G. Farin, and J. Kahmann, A Survey of Curve and Surface Methods in CAGD,Computer-Aided Geometric Design,1 (1984), 1–60.

    Article  MATH  Google Scholar 

  7. I. T. Chappel, The Use of Vectors to Simulate Material Removed by Numerically Controlled Milling,Computer-Aided Design,15(3) (1983), 156–158.

    Article  Google Scholar 

  8. S. A. Coons, Surfaces for Computer-Aided Design of Space Forms, Tech. Rep. MAC-TR-41, MIT, Cambridge, MA, June 1967.

    Google Scholar 

  9. R. L. Drysdale and R. B. Jerard, Discrete Simulation of NC Machining,Proceedings of the Third Annual ACM Symposium on Computational Geometry, June 1987, 126–135.

  10. J. P. Duncan and S. G. Mair,Sculptured Surfaces in Engineering and Medicine, Cambridge University Press, Cambridge, 1983.

    Google Scholar 

  11. A. R. Forrest, On the Rendering of Surfaces,ACM SIGGRAPH,13 (1979), 253–259.

    Article  Google Scholar 

  12. R. Fridshal, K. P. Cheng, D. Duncan, and W. Zucker, Numerical Control Part Program Verification System,Proceedings of Conference on CAD/CAM Technology in Mechanical Engineering, MIT, March 1982, MIT Press, Cambridge, MA, 236–254.

    Google Scholar 

  13. I. D. Faux and M. J. Pratt,Computational Geometry for Design and Manufacture, Ellis Horwood, Chichester, 1979.

    MATH  Google Scholar 

  14. J. D. Foley and A. VanDam,Fundamentals of Interactive Computer Graphics, Addison-Wesley, Reading, MA, 1982.

    Google Scholar 

  15. D. D. Grossman, Opportunities for Research on Numerical Control Machining,Communications of the ACM,29(6) (1986), 515–522.

    Article  Google Scholar 

  16. W. J. Gordon and R. F. Riesenfeld, B-Spline Curves and Surfaces, inComputer-Aided Geometric Design, R. Barnhill and R. Riesenfeld, eds., Academic Press, New York, 1974, 95–126.

    Google Scholar 

  17. M. P. Groover and E. W. Zimmers,CAD/CAM: Computer-Aided Design and Manufacturing, Prentice-Hall, Englewood Cliffs, NJ, 1984.

    Google Scholar 

  18. W. A. Hunt and H. B. Voelcker, An Exploratory Study of Automatic Verification of Programs for Numerically Controlled Machine Tools, Production Automation Project Tech. Memo. No. 34, University of Rochester, January 1982.

  19. R. B. Jerard, R. L. Drysdale, and K. Hauck, The Use of Computer Graphics as a Tool for Detecting Errors in Numerical Control Machining of Sculptured Surfaces,Proceedings of NCGA's Computer Graphics '87, March 1987, 290–299.

  20. R. B. Jerard, R. L. Drysdale, K. Hauck, B. Schaudt, and J. Magewick, Methods for Detecting Errors in Numerically Controlled Machining of Sculptured Surfaces,IEEE Computer Graphics and Applications, to appear.

  21. R. B. Jerard, K. Hauck, and R. L. Drysdale, Simulation of Numerical Control Machining of Sculptured Surfaces, Paper no. 86057, 15th International Symposium on Automotive Technology and Automation (ISATA), Flims, Switzerland, October 6–10, 1986.

  22. B. C. Kuttner, D. S. Majcher, and P. B. Snedecor, Systematic Processing: An Approach to Fully Automatic NC Tool Path Generation,Proceedings of Autofact '85 Conference, SME, November 1985, 18-7–18-22.

  23. A. E. Middleditch, Survey of Numerical Controller Technology, Production Automation Project TR-1-D, University of Rochester, August 1973.

  24. J. H. Oliver, Graphical Verification of Numerically Controlled Milling Programs for Sculptured Surface Parts, Ph.D. Thesis, Michigan State University, 1986.

  25. J. H. Oliver and E. D. Goodman, Color Graphic Verification of NC Milling Programs for Sculptured Surfaces,Proceedings of the 10th Annual Automotive Computer Graphics Conference and Exposition, Engineering Society of Detroit, December 1985.

  26. D. F. Rogers and J. A. Adams,Mathematical Elements for Computer Graphics, McGraw-Hill, New York, 1976.

    Google Scholar 

  27. S. M. Staley, R. B. Jerard, and P. R. White, Computer-Aided Design of Curved Surfaces with Automatic Model Generation,Trans. ASME J. Mech. Design,104(4) (1982), 817–824.

    Article  Google Scholar 

  28. D. L. Toth, On Ray Tracing Parametric Surfaces,ACM SIGGRAPH,19(3) (1985), 171–179.

    Article  Google Scholar 

  29. T. Van Hook, Real-Time Shaded NC Milling Display,ACM SIGGRAPH,20(4) (1986), 15–20.

    Article  Google Scholar 

  30. H. B. Voelcker and W. A. Hunt, The Role of Solid Modeling in Machining—Process Modeling and NC Verification, SAE Technical Paper 810195, 1981.

  31. W. P. Wang and K. K. Wang, Geometric Modeling for Swept Volume of Moving Solids,IEEE Computer Graphics and Applications,6(12) (1986), 8–17.

    Article  Google Scholar 

  32. D. Zhang and A. Bowyer, CSG Set-Theoretic Solid Modeling and NC Machining of Blend Surfaces,Proceedings of the 2nd Annual ACM Conference on Computational Geometry, June 1986, 236–245.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Dartmouth College, 03755, Hanover, NH, USA

    Robert L. (Scot) Drysdale III, Barry Schaudt & Ken Hauck

  2. Department of Mechanical Engineering, University of New Hampshire, 032824, Durham, NH, USA

    Robert B. Jerard

Authors
  1. Robert L. (Scot) Drysdale III
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robert B. Jerard
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Barry Schaudt
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ken Hauck
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by Chee-Keng Yap.

This research was supported in part by the National Science Foundation under Contract No. DMC 8512621 and by the Ford Motor Company.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Drysdale, R.L.(., Jerard, R.B., Schaudt, B. et al. Discrete simulation of NC machining. Algorithmica 4, 33–60 (1989). https://doi.org/10.1007/BF01553878

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01553878

Key words

Search

Navigation