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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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
Marciniak K (1991) Geometric modelling for numerically controlled machining. Oxford University Press, Oxford, UK
Stute G, Storr A, Sielaff W (1979) NC programming of ruled surface for five axis machining. Ann CIRP 28(1):267–271
Liu X (1995) Five-axis NC cylindrical milling of sculptured surfaces. Computer Aided Design 27(12):887–894
Rehsteiner F, Renker HJ (1993) Collision-free five-axis milling of twisted ruled surfaces. CIRP Ann 42(1):457–461
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
Tsay DM, Her MJ (2001) Accurate 5-axis machining of twisted ruled surfaces. J Manuf Sci Eng 123:734–738
Bedi S, Mann S, Menzel C (2003) Flank milling with flat end cutters. Computer Aided Design 35:293–300
Menzel C, Bedi S, Mann S (2004) Triple tangent flank milling of ruled surfaces. Comp Aided Des 36:289–296
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
Li CG, Bedi S, Mann S (2006) Flank milling surface design with the least square approach. WSEAS Transact Math 7(5):844–852
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
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
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
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
Elber G, Fish R (1997) 5-Axis freeform surface milling using piecewise ruled surface approximation. ASME 119:383–387
Yang J, Abdel-Malek K (2005) Approximate swept volumes of NURBS surfaces or solids. Comp Aided Geom Des 22:1–26
Mann S, Bedi S (2001) Generalization of the imprint method to general surfaces of revolution for NC machining. Comp Aided Des 34:373–378
Li CG, Mann S, Bedi S (2005) Error measurements for flank milling. Comp Aided Des 37:1459–1468
Lartigue C, Duc E, Affouard A (2003) Tool path deformation in 5-axis flank milling using envelop surface. Comp Aided Des 35:375–382
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
Farin G (2002) Curves and surfaces for computer-aided geometric design: a practical guide. Academic Press, New York, USA
Li CG, Bedi S, Mann S (2007) Flank millable surface design in 5-axis machining. International Conference on Smart Machining Systems. Gaithersburg, Maryland, USA.
Author information
Authors and Affiliations
Corresponding author
Rights 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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-011-3712-9