A new iso-parametric machining algorithm for free-form surface

Abstract

In this paper, a new iso-parametric tool path generation technique has been presented for machining truncated free-form surfaces by means of re-parameterisation. Three methods of re-parameterisation have been discussed, namely, the Coons method, partial differential equation method and the newly developed ‘Boundary Interpolation method.’ Tool paths have been generated based on the iso-parametric curves produced by re-parameterisation. The complete mathematical formulations have been given and subsequently their applications have been studied through some typical cases. Case studies show that the Coons and Laplace partial differential equation have some drawbacks in generating tool paths when the surface boundaries are irregular but the new Boundary Interpolation algorithm gives smooth and efficient iso-parametric tool paths by eliminating the problems like overcrossing (in case of Coons method) and uneven distribution of iso-parametrics (in case of Laplace partial differential equation method).

Keywords

Surface machining iso-parametric tool path interpolation parameterisation

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References

Suresh

Yang

. Constant scallop-height machining of free-form Surfaces. ASME J Eng Ind 1994; 116: 253–259.

Ding

Yang

DCH

Han

. Boundary-conformed machining of turbine blades. Proc IMechE, Part B: J Engineering Manufacture 2005; 219: 255–263.

George

Babu

. On the effective tool path planning algorithms for sculptured surface manufacture. Computers Ind Engg 1995; 28: 823–836.

Huang

Oliver

. Non-constant parameter NC tool path generation of sculptured surfaces. Int J Adv Manuf Technology 1994; 9: 281–290.

. A geometric approach to boundary-conformed tool path generation. Computer-Aided Design 2007; 39: 941–952.

Feng

. Constant scallop-height tool path generation for three axis sculpture surface machining. Computer-Aided Design 2002; 34: 647–654.

Loney

Ozsoy

. NC machining of free form surfaces. Computer Aided Design 1987; 19: 85–90.

Zhang

Nee

AYC

Fuh

JYH

. An efficient CC-curve tool path regeneration algorithm for sculptured surface machining. Proc IMechE, Part B: J Engineering Manufacture 2004; 218: 389–402.

Mortenson Michael

. Geometric modeling, New York, Chichester, Weinheim, Brisbane, Singapore, Toronto: John Wiley & Sons, Inc., 1985.

10.

Coons

. Surfaces for computer-aided design of space figures. MIT ESL 19649442-M-139.

11.

Farin

. Curves and surfaces for computer aided geometric design, a practical guide, New York: Academic Press, Inc., 1988.

12.

Sarkar

Dey

. Construction of 2-D parametric surfaces bounded with four irregular curves. Int J Computer Aided Engg Technol 2012; 4: 474–487.

13.

Peter

. Interactive computer graphics application of the bicubic parametric surface to engineering design problems. McDonnell Douglas Automation Company, St Louis, Missouri, presented at SIAM 1973 National Meeting, Hampton, 1973, pp. 18–21.

14.

Sarkar S and Dey PP. A new boundary interpolation technique for parameterisation of planar surfaces with four arbitrary boundary curves. Proc of the IMechE, Part C: J. Mechanical Engineering Science 2012; 227(6): 1280–1290.

15.

Smith Robert

. Three-dimensional algebraic grid generation. AIAA 6th Computational Fluid Dynamics Conference, Danvers, Massachusetts, 1983.

16.

Soni

. Grid generation for internal flow configurations. Comput Math Appl 1992; 24: 191–201.

17.

Soni

. Grid generation: past, present, and future. Appl Numer Math 2000; 32: 361–369.

18.

Szilva´si-Nagy

Szabo

. Generalization of Coons’ construction. Comput Graph 2006; 30: 588–597.

19.

Wang

CCL

Tang

. Algebraic grid generation on trimmed parametric surface using non-self-overlapping Coons patch mapping. Int J Numer Meth Engg 2004; 60: 1259–1286.

20.

Wang

CCL

Tang

. Non-self-overlapping structured grid generation on an n-sided surface. Int J Numerical Meth Fluid 2004; 46: 961–982.

21.

Yamaguchi

. Curves and surfaces in computer aided geometric design, Heidelberg: Springer-Verlag, 1988.

22.

Zhang

You

. Analytical C2 smooth blending surfaces. Future Gen Comput Sys 2004; 20: 1317–1326.

23.

Hsu

Lee

. A numerical technique for two-dimensional grid generation with grid control at all of the boundaries. J Comput Phys 1992; 96: 451–469.

24.

Westgaard

Nowacki

. Construction of fair surfaces over irregular meshes. ASME J Mech Des 2001; 1: 376–384.

25.

Cebeci

Shao

Kafyeke

. Computational fluid dynamics for engineers: From Panel to Navier-Stokes Methods with Computer Programs, Long Beach, California: Horizons Publishing Inc., 2005.

26.

Thompson

Warsi

ZUA

Mastin

. Numerical grid generation, foundations and applications, North Holland: Elsevier, 1985.

27.

Hoffmann Klaus

Chiang Steve

. Computational fluid dynamics for engineers, Wichita, Kansas, USA: Engineering Education System, 1989.

28.

Vladimir

Liseikin . Grid generation methods, Dordrecht Heidelberg London New York: Springer, 2010.

29.

Marsh

. Applied geometry for computer graphics and CAD, London: Springer-Verlag Limited, 2005.

30.

Faux

Pratt

. Computational geometry for design and manufacture, Chichester: Ellis Horwood, 1979.

31.

Stoker

. Differential geometry, New York, London, Sydney, Toronto: Wiley-Interscience, 1989.

32.

Yamaguchi

. Curves and Surfaces in Computer Aided Geometric Design 1988(Springer).