NURBS approximation to the flank-milled surface swept by a cylindrical NC tool

The International Journal of Advanced Manufacturing Technology volume 61, pages35–51(2012)Cite this article

Abstract

In this paper, a method to approximate the flank-milled surface swept by a cylindrical cutter with a non-uniform rational basis spline (NURBS) surface is presented. The swept surface produced by the moving tool can be calculated as a collection of points organized as a series of grazing curves along the surface. The generated NURBS surface closely matches the grazing surface. The deviation between this surface and the grazing surface is calculated and is controlled by increasing the number of control points used to represent the surface.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

US$ 39.95

Tax calculation will be finalised during checkout.

References

  1. 1.

    Rubio W, Lagarrigue P, Dessein G, Pastor F (1998) Calculation of tool paths for a torus mill on free-form surfaces on five-axis machines with detection and elimination of interference. Int J Adv Manuf Technol 14:13–20

    Article  Google Scholar 

  2. 2.

    Marciniak K (1991) Geometric modelling for numerically controlled machining. Oxford University Press, Oxford, UK

    MATH  Google Scholar 

  3. 3.

    Stute G, Storr A, Sielaff W (1979) NC programming of ruled surface for five axis machining. Ann CIRP 28(1):267–271

    Google Scholar 

  4. 4.

    Liu X (1995) Five-axis NC cylindrical milling of sculptured surfaces. Computer Aided Design 27(12):887–894

    Article  Google Scholar 

  5. 5.

    Rehsteiner F, Renker HJ (1993) Collision-free five-axis milling of twisted ruled surfaces. CIRP Ann 42(1):457–461

    Article  Google Scholar 

  6. 6.

    Bohez ELJ, Senadhera SDR, Pole K, Duflou JR, Tar T (1997) A geometric modelling and five-axis machining algorithm for centrifugal impellers. J Manuf Syst 16(6):422–463

    Article  Google Scholar 

  7. 7.

    Tsay DM, Her MJ (2001) Accurate 5-axis machining of twisted ruled surfaces. J Manuf Sci Eng 123:734–738

    Article  Google Scholar 

  8. 8.

    Bedi S, Mann S, Menzel C (2003) Flank milling with flat end cutters. Computer Aided Design 35:293–300

    Article  Google Scholar 

  9. 9.

    Menzel C, Bedi S, Mann S (2004) Triple tangent flank milling of ruled surfaces. Comp Aided Des 36:289–296

    Article  Google Scholar 

  10. 10.

    Li CG, Bedi S, Mann S (2006) Flank milling of ruled surface with conical tools—an optimization approach. Int J Adv Manuf Technol 29(11–12):1115–1124

    Article  Google Scholar 

  11. 11.

    Li CG, Bedi S, Mann S (2006) Flank milling surface design with the least square approach. WSEAS Transact Math 7(5):844–852

    Google Scholar 

  12. 12.

    Redonnet J-M, Rubio W, Dessein G (1998) Side milling of ruled surfaces: optimum positioning of the milling cutter and calculation of interference. Advanced Manufacturing Technology 14(7):459–465

    Article  Google Scholar 

  13. 13.

    Monies F, Redonnet J-M, Rubio W, Lagarrigue P (2000) Improved position of a conical mill for machining ruled surfaces: application to turbine blades. J Eng Manufac 214:625–634, Part B

    Article  Google Scholar 

  14. 14.

    Monies F, Rubio W, Redonnet J-M, Lagarrigue P (2001) Comparative study of interference caused by different position settings of a conical milling cutter on a ruled surface. Proceedings of the Institution of Mechanical Engineers. B JNL Eng Manufact 215(9):1305

    Article  Google Scholar 

  15. 15.

    Monies F, Felices JN, Rubio W, Redonnet J-M, Lagarrigue P (2002) Five-axis NC milling of ruled surface: optimal geometry of a conical tool. Int J Prod Res 40(12):2901–2922

    Article  Google Scholar 

  16. 16.

    Elber G, Fish R (1997) 5-Axis freeform surface milling using piecewise ruled surface approximation. ASME 119:383–387

    Google Scholar 

  17. 17.

    Yang J, Abdel-Malek K (2005) Approximate swept volumes of NURBS surfaces or solids. Comp Aided Geom Des 22:1–26

    MathSciNet  MATH  Article  Google Scholar 

  18. 18.

    Mann S, Bedi S (2001) Generalization of the imprint method to general surfaces of revolution for NC machining. Comp Aided Des 34:373–378

    Article  Google Scholar 

  19. 19.

    Li CG, Mann S, Bedi S (2005) Error measurements for flank milling. Comp Aided Des 37:1459–1468

    Article  Google Scholar 

  20. 20.

    Lartigue C, Duc E, Affouard A (2003) Tool path deformation in 5-axis flank milling using envelop surface. Comp Aided Des 35:375–382

    Article  Google Scholar 

  21. 21.

    Senatore J, Monies F, Redonnet J-M, Rubio W (2005) Analysis of improved positioning in five-axis ruled surface milling using envelop surface. Comp Aided Des 37:989–998

    Article  Google Scholar 

  22. 22.

    Farin G (2002) Curves and surfaces for computer-aided geometric design: a practical guide. Academic Press, New York, USA

    Google Scholar 

  23. 23.

    Li CG, Bedi S, Mann S (2007) Flank millable surface design in 5-axis machining. International Conference on Smart Machining Systems. Gaithersburg, Maryland, USA.

Download references

Author information

Affiliations

  1. Mechanical and Mechatronics Engineering Department, University of Waterloo, Ontario, Canada, N2L3G1

    Chenggang Li & Sanjeev Bedi

  2. David R. Cheriton School of Computer Science, University of Waterloo, Ontario, Canada, N2L3G1

    Stephen Mann

Authors
  1. Chenggang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sanjeev Bedi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Stephen Mann
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stephen Mann.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Li, C., Bedi, S. & Mann, S. NURBS approximation to the flank-milled surface swept by a cylindrical NC tool. Int J Adv Manuf Technol 61, 35–51 (2012). https://doi.org/10.1007/s00170-011-3712-9

Download citation

Keywords

  • Curved surface design
  • Flank milling
  • Surface numerical analysis
  • Surface error control