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Generating spiral tool path to machine free-form surface with complex topology based on fusing constraint mapping and enriched Voronoi diagram

  • Zhiping Liu
  • Xiongbing Li
  • Bing YiEmail author
ORIGINAL ARTICLE
  • 15 Downloads

Abstract

Although there are methods to machine free-form surfaces, serious distortion in the concave–convex characteristic of the flattened-plane boundary, high deformation of the surface geometry, and single limitation of the surface topology are usually produced. Thus, a novel surface flattening method is proposed in this paper to retain the concave–convex characteristic and reduce the deformation, and a spiral path is generated to machine the free-form surface with various topologies. The machined surface is mapped to a planar region with a free boundary using a fusing constraint mapping method. First, the spring-mass-based stretching constraint is used to minimize the length differences of the triangular sides, which are caused by surface flattening. Subsequently, in order to flatten surfaces with an isometric deformation, we perform this operation under the constraint of hinge-based bending. Eventually, the global constraint, the minimization of the global energy, is employed to acquire a less distorted plane. Then, to generate a planar spiral path fit for machining various planes, which are concave, convex, simply-connected, or multiply connected, enrichment of the conventional Voronoi diagram, interpolation between the wave fronts, and rounding of the spiral polyline are implemented. For machining a free-form surface, by inversely mapping the planar path, a spiral tool path is planned. Experimental results are given to illustrate the effectiveness of the presented methods.

Keywords

Fusing constraint mapping Enriched Voronoi diagram Free-form surface machining Error analysis 

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Notes

Acknowledgments

The authors would like to express their gratitude to Travis D. Ashworth for many useful comments on English writing.

Funding information

This work is supported by the National Natural Science Foundation of China under Grant No.51605495, the Fundamental Research Funds for the Central Universities of Central South University under Grant NO.2017zzts195, the International Postdoctoral Exchange Fellowship Program Grant NO.2017[59], and Research on Laboratory Construction and Management of Central South University Program NO. 201719.

References

  1. 1.
    Luo S, Dong Z, Jun MBG (2016) Chip volume and cutting force calculations in 5-axis CNC machining of free-form surfaces using flat-end mills. Int J Adv Manuf Technol 90(1–4):1–10.  https://doi.org/10.1007/s00170-016-9423-5 CrossRefGoogle Scholar
  2. 2.
    Zhao J, Zou Q, Li L, Zhou B (2015) Tool path planning based on conformal parameterization for meshes. Chinese J Aeronaut 26(5):1555–1563.  https://doi.org/10.1016/j.cja.2015.06.005 CrossRefGoogle Scholar
  3. 3.
    Sun Y, Guo D, Jia Z, Wang H (2006) Iso-parametric tool path generation from triangular meshes for free-form surface machining. Int J Adv Manuf Technol 28(7):721–726.  https://doi.org/10.1007/s00170-004-2437-4 CrossRefGoogle Scholar
  4. 4.
    Xu J, Sun Y, Wang S (2013) Tool path generation by offsetting curves on polyhedral surfaces based on mesh flattening. Int J Adv Manuf Technol 64(9):1201–1212.  https://doi.org/10.1007/s00170-012-4075-6 CrossRefGoogle Scholar
  5. 5.
    Zhu H, Liu Z, Fu J (2011) Spiral tool-path generation with constant scallop height for sheet metal CNC incremental forming. Int J Adv Manuf Technol 54(9):911–919.  https://doi.org/10.1007/s00170-010-2996-5 CrossRefGoogle Scholar
  6. 6.
    Lee E (2003) Contour offset approach to spiral toolpath generation with constant scallop height. Comput Aided Design 35(6):511–518.  https://doi.org/10.1016/S0010-4485(01)00185-3 CrossRefGoogle Scholar
  7. 7.
    Hauth S, Linsen L (2011) Double-spiral tool path in configuration space. Int J Adv Manuf Technol 54(9):1011–1022.  https://doi.org/10.1007/s00170-010-3004-9 CrossRefGoogle Scholar
  8. 8.
    Sun YW, Guo DM, Jia ZY (2006) Spiral cutting operation strategy for machining of sculptured surfaces by conformal map approach. J Mater Process Tech 180(1–3):74–82.  https://doi.org/10.1016/j.jmatprotec.2006.05.004 CrossRefGoogle Scholar
  9. 9.
    Ren F, Sun Y, Guo D (2009) Combined reparameterization-based spiral toolpath generation for five-axis sculptured surface machining. Int J Adv Manuf Technol 40(7):760–768.  https://doi.org/10.1007/s00170-008-1385-9 CrossRefGoogle Scholar
  10. 10.
    Sun Y, Ren F, Zhu X, Guo D (2012) Contour-parallel offset machining for trimmed surfaces based on conformal mapping with free boundary. Int J Adv Manuf Technol 60(1):261–271.  https://doi.org/10.1007/s00170-011-3577-y CrossRefGoogle Scholar
  11. 11.
    Hauth S, Linsen L (2011) Double-spiral tool path in configuration space. Int J Adv Manuf Technol 54(9–12):1011–1022.  https://doi.org/10.1007/s00170-010-3004-9 CrossRefGoogle Scholar
  12. 12.
    Zhou B, Zhao J, Li L (2015) CNC double spiral tool-path generation based on parametric surface mapping ☆. Comput Aided Design 67–68(C):87–106. doi:  https://doi.org/10.1016/j.cad.2015.06.005
  13. 13.
    Abrahamsen M (2014). Spiral toolpaths for high-speed machining of 2D pockets with or without islands. preprint arXiv: cs.CG/1412.5034Google Scholar
  14. 14.
    Wang C, Smith S, Yuen M (2002) Surface flattening based on energy model. Comput Aided Design 34(11):823–833 doi: s0010-4485(01)00150-6CrossRefGoogle Scholar
  15. 15.
    Martin S, Thomaszewski B, Grinspun E, Gross M (2011) Example-based elastic materials. Acm T Graphic 30(4):72.  https://doi.org/10.1145/1964921.1964967 CrossRefGoogle Scholar
  16. 16.
    Liu T, Bargteil A W, O'Brien J F, Kavan L (2013). Fast simulation of mass-spring systems. Acm T Graphic 32(6):209:1–7. doi:  https://doi.org/10.1145/2508363.2508406
  17. 17.
    Botsch M (2010) Polygon mesh processing. Taylor & Francis Ltd.Google Scholar
  18. 18.
    Held M, Spielberger C (2009) A smooth spiral tool path for high speed machining of 2D pockets. Comput Aided Design 41(7):539–550.  https://doi.org/10.1016/j.cad.2009.04.002 CrossRefGoogle Scholar
  19. 19.
    Chuang JJ, Yang DCH (2007) A Laplace-based spiral contouring method for general pocket machining. Int J Adv Manuf Technol 34(7–8):714–723.  https://doi.org/10.1007/s00170-006-0648-6 CrossRefGoogle Scholar
  20. 20.
    Held M, Spielberger C (2014) Improved spiral high-speed machining of multiply-connected pockets. Comput Aided Design Appl 11(3):346–357.  https://doi.org/10.1080/16864360.2014.863508 CrossRefGoogle Scholar
  21. 21.
    Zhou B, Zhao J, Liu W, Li L (2013) Generation method for five-axis NC spiral tool path based on parametric surface mapping. J Syst Sci Complex 26(5):676–694.  https://doi.org/10.1007/s11424-013-3174-2 CrossRefzbMATHGoogle Scholar
  22. 22.
    Carmo M P D (1976) Differential geometry of curves and surfaces. Computer Aided Engineering Design 2(4):273–275. ISBN: 978-0-13-212589-5Google Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Traffic and Transportation EngineeringCentral South UniversityChangshaChina
  2. 2.University of MichiganAnn ArborUSA

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