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An efficient greedy strategy for five-axis tool path generation on dense triangular mesh

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Abstract

This paper presents an efficient greedy strategy for generating tool paths on triangular meshes with consideration of axis kinematics. Curvatures at the vertices of the triangular mesh are estimated, which are used to determine the cutting strip width and maximum feedrate. Starting from a given CC point, the next CC point is chosen to be the one which maximizes the feedrate limit at the current CC point and minimizes the cutting strip overlaps. This process is carried out iteratively until all the mesh vertices are cut. Simulation results are presented to illustrate the feasibility of the algorithm.

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Abbreviations

x 1,x 2,⋯ ,x N :

Mesh vertices

n i :

Normal vector at x i

κ i j :

Normal curvature along x j −x i

H i :

Mean curvature at x i

r :

Ball-end mill radius

h :

Scallop height limit

d i j :

Strip width when cutting along x j −x i

P=[P x ,P y ,P z ]T :

Tool center position

O=[O i ,O j ,O k ]T :

Tool orientation

q=[X,Y,Z,A,C]T :

Five-axis position command

F m a x :

Feedrate limit

V m a x,τ :

Axis velocity limit

A m a x,τ :

Axis acceleration limit

f k i j :

Maximum feedrate at x i

\(\boldsymbol {c}^{i}_{1}, \boldsymbol {c}^{i}_{2}, \cdots , \boldsymbol {c}^{i}_{j}, \boldsymbol {c}^{i}_{j+1}, \cdots \) :

Sequence of CC points on the ith tool path

References

  1. Elber G, Cohen E (1994) Toolpath generation for freeform surface models. Comput Aided Des 26(6):490–496

    Article  MATH  Google Scholar 

  2. Wang YM, Tang XS (1999) Five-axis NC machining of sculptured surfaces. Int J Adv Manuf Tech 15(1):7–14

    Article  MATH  Google Scholar 

  3. Seok Suh Y, Lee K (1990) NC milling tool path generation for arbitrary pockets defined by sculptured surfaces. Comput Aided Des 22(5):273–284

    Article  Google Scholar 

  4. Ding S, Mannan M, Poo AN, Yang D, Han Z (2003) Adaptive isoplanar tool path generation for machining of free-form surfaces. Comput Aided Des 35(2):141–153

    Article  Google Scholar 

  5. Suresh K, Yang D (1994) Constant scallop-height machining of free-form surfaces. J Eng Ind 116(2):253–259

    Article  Google Scholar 

  6. Lo C-C (1999) Efficient cutter-path planning for five-axis surface machining with a flat-end cutter. Comput Aided Des 31(9):557–566

    Article  MATH  Google Scholar 

  7. Lee E (2003) Contour offset approach to spiral toolpath generation with constant scallop height. Comput Aided Des 35(6):511–518

    Article  Google Scholar 

  8. Kim T, Sarma SE (2002) Toolpath generation along directions of maximum kinematic performance; a first cut at machine-optimal paths. Comput Aided Des 34(6):453–468

    Article  Google Scholar 

  9. Castagnetti C, Duc E, Ray P (2008) The domain of admissible orientation concept: a new method for five-axis tool path optimisation. Comput Aided Des 40(9):938–950

    Article  Google Scholar 

  10. Lavernhe S, Tournier C, Lartigue C (2008) Optimization of 5-axis high-speed machining using a surface based approach. Comput Aided Des 40(10):1015–1023

    Article  Google Scholar 

  11. Wang N, Tang K (2008) Five-axis tool path generation for a flat-end tool based on iso-conic partitioning. Comput Aided Des 40(12):1067–1079

    Article  Google Scholar 

  12. Hu P, Tang K (2011) Improving the dynamics of fiveaxis machining through optimization of workpiece setup and tool orientations. Comput Aided Des 43(12):1693–1706

    Article  Google Scholar 

  13. Kim S-J, Yang M-Y (2006) A CL surface deformation approach for constant scallop height tool path generation from triangular mesh. Int J Adv Manuf Tech 28(3–4):314–320

    Article  Google Scholar 

  14. 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 Tech 28(7–8):721–726

    Google Scholar 

  15. Lee S-G, Kim H-C, Yang M-Y (2008) Mesh-based tool path generation for constant scallop-height machining. Int J Adv Manuf Tech 37(1–2):15–22

    Article  Google Scholar 

  16. Xu J, Sun Y, Wang S (2013) Tool path generation by offsetting curves on polyhedral surfaces based on mesh flattening. Int J Adv Manuf Tech 64(9–12):1201–1212

    Article  Google Scholar 

  17. Taubin G (1995) Estimating the tensor of curvature of a surface from a polyhedral approximation. In: Proceedings, Fifth International Conference on Computer Vision, IEEE, pp 902–907

  18. Meyer M, Desbrun M, Schröder P, Barr AH (2002) Discrete differential-geometry operators for triangulated 2-manifolds. Visualization and Mathematics 3(2):52–58

    Google Scholar 

  19. Lin R, Koren Y (1996) Efficient tool-path planning for machining free-form surfaces. J Eng Ind Trans ASME 118:20–28

    Article  Google Scholar 

  20. Zhang K, Yuan C-M, Gao X-S (2013) Efficient algorithm for time-optimal feedrate planning and smoothing with confined chord error and acceleration. Int J Adv Manuf Tech 66(9):1685–1697

    Article  Google Scholar 

  21. Yuen A, Zhang K, Altintas Y (2013) Smooth trajectory generation for five-axis machine tools. Int J Mach Tool Manu 71:11–19

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Hong Kong, Hong Kong

    Ke Zhang & Kai Tang

Authors
  1. Ke Zhang
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  2. Kai Tang
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Correspondence to Kai Tang.

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Zhang, K., Tang, K. An efficient greedy strategy for five-axis tool path generation on dense triangular mesh. Int J Adv Manuf Technol 74, 1539–1550 (2014). https://doi.org/10.1007/s00170-014-6083-1

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  • DOI: https://doi.org/10.1007/s00170-014-6083-1

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