Abstract
In CNC machining, the tool path planning of the cutter plays an important role. In this paper, we generate a space-filling and continuous tool path for free-form surface represented by the triangular mesh with a confined scallop height. The tool path is constructed from connected Fermat spirals (CFS) but with fewer inflection points. Comparing with the newly developed CFS method, only about half of the number of inflection points are involved. Moreover, the kinematic constraints are simultaneously taken into account to increase the feedrates in machining. Finally, we use a micro-line trajectory technique to smooth the tool path. Experimental results and physical cutting tests are provided to illustrate and clarify our method.
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References
Anotaipaiboon, W., Makhanov, S.S.: Curvilinear space-filling curves for five-axis machining. Comput. Aided Des. 40(3), 350–367 (2008). https://doi.org/10.1016/j.cad.2007.11.007
Anotaipaiboon, W., Makhanov, S.S.: Tool path generation for five-axis NC machining using adaptive space-filling curves. Int. J. Prod. Res. 43(8), 1643–1665 (2005). https://doi.org/10.1080/00207540412331322948
Au, C.: A path interval generation algorithm in sculptured object machining. Int. J. Adv. Manuf. Technol. 17, 558–561 (2001). https://doi.org/10.1007/s001700170138
Chen, L., Zhang, R., Tang, K., Hu, P., Zhao, P., Li, Z., Han, Z.: A spiral-based inspection path generation algorithm for efficient five-axis sweep scanning of freeform surfaces. Comput. Aided Des. 124, 102838 (2020). https://doi.org/10.1016/j.cad.2020.102838
Chen, Y., Shen, L.Y., Yuan, C.M.: Collision and intersection detection of two ruled surfaces using bracket method. Comput. Aided Geom. Des. 28(2), 114–126 (2011). https://doi.org/10.1016/j.cagd.2010.11.002
Chiou, C.J., Lee, Y.S.: A machining potential field approach to tool path generation for multi-axis sculptured surface machining. Comput. Aided Des. 34(5), 357–371 (2002). https://doi.org/10.1016/S0010-4485(01)00102-6
Choi, B.K., Park, S.C.: A pair-wise offset algorithm for 2D point-sequence curve. Comput. Aided Des. 31(12), 735–745 (1999). https://doi.org/10.1016/S0010-4485(99)00060-3
Cox, J.J., Takezaki, Y., Ferguson, H.R.P., Kohkonen, K.E., Mulkay, E.L.: Space-filling curves in tool-path applications. Comput. Aided Des. 26(3), 215–224 (1994). https://doi.org/10.1016/0010-4485(94)90044-2
Crane, K., Weischedel, C., Wardetzky, M.: Geodesics in heat: A new approach to computing distance based on heat flow. ACM Trans. Graph (2013). https://doi.org/10.1145/2516971.2516977
Elber, G., Cohen, E.: Toolpath generation for freeform surface models. Comput. Aided Des. 26, 490–496 (1994). https://doi.org/10.1016/0010-4485(94)90070-1
Farouki, R.T., Tsai, Y.F., Yuan, G.F.: Contour machining of free-form surfaces with real-time PH curve CNC interpolators. Comput. Aided Geom. Des. 16(1), 61–76 (1999). https://doi.org/10.1016/S0167-8396(98)00032-6
Giri, V., Bezbaruah, D., Bubna, P., Choudhury, A.R.: Selection of master cutter paths in sculptured surface machining by employing curvature principle. Int, J. Mach. Tools Manuf., 45(10):1202–1209, (2005). ISSN 0890-6955. https://doi.org/10.1016/j.ijmachtools.2004.12.008
Gu, X., Yau, S.T.: Computational Conformal Geometry. Higher Education Press, (2020)
Held, M., Lukács, G., Andor, L.: Pocket machining based on contour-parallel tool paths generated by means of proximity maps. Comput. Aided Des. 26(3), 189–203 (1994). https://doi.org/10.1016/0010-4485(94)90042-6
Held, M.: Voronoi diagrams and offset curves of curvilinear polygons. Comput. Aided Des. 30(4), 287–300 (1998). https://doi.org/10.1016/S0010-4485(97)00071-7
Hu, P., Chen, L., Tang, K.: Efficiency-optimal iso-planar tool path generation for five-axis finishing machining of freeform surfaces. Comput. Aided Des. 83, 33–50 (2017). https://doi.org/10.1016/j.cad.2016.10.001
Huo, G., Jiang, X., Su, C., Lu, Z., Sun, Y., Zheng, Z., Xue, D.: CNC tool path generation for freeform surface machining based on preferred feed direction field. Int. J. Prec. Eng. Manuf. 20, 777–790 (2019). https://doi.org/10.1007/s12541-019-00084-2
Kim, B.H., Choi, B.K.: Machining efficiency comparison direction-parallel tool path with contour-parallel tool path. Comput. Aided Des. 34(2), 89–95 (2002). https://doi.org/10.1016/S0010-4485(00)00139-1
Lee, E.: Contour offset approach to spiral toolpath generation with constant scallop height. Comput. Aided Des. 35(6), 511–518 (2003). https://doi.org/10.1016/S0010-4485(01)00185-3
Lee, Y., Ji, H.: Surface interrogation and machining strip evaluation for 5-axis CNC die and mold machining. Int. J. Prod. Res. 35(1), 225–252 (1997). https://doi.org/10.1080/002075497196064
Lee, Y.S.: Non-isoparametric tool path planning by machining strip evaluation for 5-axis sculptured surface machining. Comput. Aided Des. 30(7), 559–570 (1998). https://doi.org/10.1016/S0010-4485(98)00822-7
Liang, F., Kang, C., Lu, Z., Fang, F.: Iso-scallop tool path planning for triangular mesh surfaces in multi-axis machining. Robot. Comput. Integ. Manuf. 72, 102206 (2021). https://doi.org/10.1016/j.rcim.2021.102206
Lin, R., Koren, Y.Y.: Efficient tool-path planning for machining free-form surfaces. J. Eng. Ind. 118(1), 20–28 (1996). https://doi.org/10.1115/1.2803642
Loney, G.C., Ozsoy, T.M.: NC machining of free form surfaces. Comput. Aided Des. 19(2), 85–90 (1987). https://doi.org/10.1016/S0010-4485(87)80050-7
Marshall, S., Griffiths, J.G.: A new cutter-path topology for milling machines. Comput. Aided Des. 26(3), 204–214 (1994). https://doi.org/10.1016/0010-4485(94)90043-4
Min, C.: A new iso-scallop height tool path planning method in three-dimensional space. Comput. Aided Draft. Des. Manuf. 22, 35–42 (2012)
Pi, J., Red, E., Jensen, G.: Grind-free tool path generation for five-axis surface machining. Comput. Integr. Manuf. Syst. 11(4), 337–350 (1998). https://doi.org/10.1016/S0951-5240(98)00033-0
Salman, M., Mansor, A., Hinduja, S., Owodunni, O.O.: Voronoi diagram-based tool path compensations for removing uncut material in 2\(\frac{1}{2}\)D pocket machining. Comput. Aided Des. 38(3), 194–209 (2006). https://doi.org/10.1016/j.cad.2005.09.001
Sarma, S.E.: The crossing function and its application to zig-zag tool paths. Comput. Aided Des. 31(4), 881–890 (1999). https://doi.org/10.1016/S0010-4485(99)00075-5
Shen, H., Li, J., Zhou, L.: Estimation of triangular mesh vertex normal vector and discrete curvature. Comput. Eng. Appl. 41(26), 12–15 (2005)
Su, C., Jiang, X., Huo, G., Sun, Y., Zheng, Z.: Initial tool path selection of the iso-scallop method based on offset similarity analysis for global preferred feed directions matching. Int. J. Adv. Manuf. Technol. 106, 2675–2687 (2020). https://doi.org/10.1007/s00170-019-04789-6
Sun, Y., Xu, J., Jin, C., Guo, D.: Smooth tool path generation for 5-axis machining of triangular mesh surface with nonzero genus. Comput. Aided Des. 79, 60–74 (2016). https://doi.org/10.1016/j.cad.2016.06.001
Taubin, G.: Estimating the tensor of curvature of a surface from a polyhedral approximation. Proc. IEEE Int. Conf. Comput. Vis. (1995). https://doi.org/10.1109/ICCV.1995.466840
Xu, J., Xu, L., Sun, Y., Lee, Y., Zhao, J.: A method of generating spiral tool path for direct three-axis computer numerical control machining of measured cloud of point. ASME J. Comput. Inf. Sci. Eng 19(4), 041015 (2019). https://doi.org/10.1115/1.4043532
Xu, K., Li, Y.: Region based five-axis tool path generation for freeform surface machining via image representation. Robot. Comput. Integ. Manuf. 57, 230–240 (2019). https://doi.org/10.1016/j.rcim.2018.12.006
Zhang, L., Sun, R., Gao, X.S., Li, H.: High speed interpolation for micro-line trajectory and adaptive real-time look-ahead scheme in CNC machining. SCI. CHINA Technol. Sci. 54(6), 1481–1495 (2011). https://doi.org/10.1007/s11431-011-4329-9
Zhao, H., Gu, F., Huang, Q.X., Garcia, J., Chen, Y., Tu, C., Benes, B., Zhang, H., Cohen-Or, D., Chen, B.: Connected fermat spirals for layered fabrication. ACM Trans. Graph (2016). https://doi.org/10.1145/2897824.2925958
Zhao, H., Zhang, H., Xin, S., Deng, Y., Tu, C., Wang, W., Cohen-Or, D., Chen, B.: DSCarver: decompose-and-spiral-carve for subtractive manufacturing. ACM Trans. Graph (2018). https://doi.org/10.1145/3197517.3201338
Zhu, H., Liu, Z., Fu, J.: Spiral tool-path generation with constant scallop height for sheet metal CNC incremental forming. Int. J. Adv. Manuf. Technol. 54(9–12), 911–919 (2011). https://doi.org/10.1007/s00170-010-2996-5
Zou, Q., Zhang, J., Deng, B., Zhao, J.: Iso-level tool path planning for free-form surfaces. Comput. Aided Des. 53, 117–125 (2014). https://doi.org/10.1016/j.cad.2014.04.006
Acknowledgements
We would like to thank Dr. Haisen Zhao for providing us the tool path point sequence in Fig. 19, and Shenyang Golding Nc Intelligence Tech. Co., Ltd for physical cutting test. This work is partially supported by Beijing Natural Science Foundation under Grant Z190004, National Key Research and Development Program of China under Grant 2020YFA0713703, NSFC(Nos. 11688101, 61872332) and Fundamental Research Funds for the Central Universities.
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Ma, HY., Yuan, CM. & Shen, LY. Tool Path Planning with Confined Scallop Height Error Using Optimal Connected Fermat Spirals. Commun. Math. Stat. 12, 55–78 (2024). https://doi.org/10.1007/s40304-021-00280-5
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DOI: https://doi.org/10.1007/s40304-021-00280-5