Volume Interior Parameterization for Automated Unified Machining Process of Freeform Surfaces
Conventional machining process of freeform surfaces usually employs three-stage machining process of roughing, semi-finishing and finishing. This multi-stage machining process has some weaknesses such as the repetition of process planning activities or heavy cutting load changes. But they can be overcome by gradually machining a stock along morphing surfaces. The generation of the morphing surfaces transforming smoothly inside the to-be-cut volume is essential for the new machining process and it can be achieved by the volume interior parameterization. This paper introduces five volume interior parameterization methods: TFI method, Laplace method, Poisson method using exponential control functions, Poisson method using arc-length based control map and weighted parametric redistribution method. Algorithms for these methods are presented, and their respective computer simulations packages are generated. Numerical examples show that the algorithms can adequately generate intermediate machining surfaces inside any arbitrary shape volume.
KeywordsVolume interior parameterization Machining Free-form surface Morphing Grid generation
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- 2.Lefebvre, P., Lauwers, B.: 3D morphing for generating intermediate roughing levels in multi-axis machining. Computer-Aided Design & Application 2(1-4), 115–123 (2005)Google Scholar
- 4.Thompson, J.F., Soni, B.K., Weatherill, N.P.: Handbook of grid generation. CRC Press (1999)Google Scholar
- 5.Hoffman, J.D.: Numerical Methods for Engineers and Scientists. McGraw-Hill (1992)Google Scholar
- 6.Hoffmann, K.A., Chiang, S.T.: Computational Fluid Dynamics for Engineers. Engineering Education System (1993)Google Scholar
- 7.Weatherill, N.P.: Grid generation, VKI-Lecture- Series 1990–06. Von Karman Institute for Fluid Dynamics (1990) Google Scholar
- 9.Thompson, J.F., Warsi, Z.U.A., Mastin, C.: Numerical grid generation, fundamental and application. North-Holland, Elsevier (1985)Google Scholar