Abstract
Most of the research on tool paths for cutting machines focuses on determining the path for contour cutting. State-of-the-art, resource-efficient sheet metal cutting technologies allow one to match the contours of the cut parts, thus reducing material waste and minimizing the cut length. However, the alignment of the boundaries of the cut contours is the source of a number of constraints formalized in terms of plane graphs: (1) ordered enclosing, (2) nonintersecting cutting path. The article considers the main data structures and algorithms used in the CAD/CAM system developed for technological preparation of cutting processes, which allows cutting plans with combined contours, as well as software that constructs a homeomorphic image of a graph to solve the problem of routing according to the cutting plan, solves this problem, and interprets the solution results.
Similar content being viewed by others
REFERENCES
Dewil, R., Vansteenwegen, P., and Cattrysse, D., A review of cutting path algorithms for laser cutters, Int. J. Adv. Manuf. Technol., 2016, vol. 87, pp. 1865–1884. https://doi.org/10.1007/s00170-016-8609-1
Makarovskikh, T.A., Panyukov, A.V., and Savitsky, E.A., Mathematical models and routing algorithms for CAD technological preparation of cutting processes, Autom. Remote Control, 2017, vol. 78, no. 4, pp. 868–882.
Makarovskikh, T. and Panyukov, A., The cutter trajectory avoiding intersections of cuts, IFAC-PapersOnLine, 2017, vol. 50, no. 1, pp. 2284–2289. https://doi.org/10.1016/j.ifacol.2017.08.226
Li, X., Liu, Zh., Wang, F., Yi, B., and Song, Y., Combining physical shell mapping and reverse-compensation optimisation for spiral machining of free-form surfaces, Int. J. Prod. Rts., 2018. https://doi.org/10.1080/00207543.2018.1512763
Makarovskikh, T. and Panyukov, A., Development of routing methods for cutting out details, CEUR Workshop Proc., 2018, vol. 2098, pp. 249–263. http://ceur-ws.org/Vol-2098/paper22.pdf
Dewil, R., Vansteenwegen, P., Cattrysse, D., Laguna, M., and Vossen, T., An improvement heuristic framework for the laser cutting tool path problem, Int. J. Prod. Rts., 2015, vol. 53, no. 6, pp. 1761–1776. https://doi.org/10.1080/00207543.2014.959268
Petunin, A. and Stylios, C., optimization models of tool path problem for CNC sheet metal cutting machines, IFAC-PapersOnLine, 2016, vol. 49, pp. 23–28. https://doi.org/10.1016/j.ifacol.2016.07.544
Petunin, A., Chentsov, A.G., and Chentsov, P.A., About routing in the sheet cutting, Bull. South Ural State Univ. Ser.: Math. Model. Program. Comput. Software, 2017, vol. 10, no. 3, pp. 25–39. https://doi.org/10.14529/mmp170303
Chentsov, A.G., Grigoryev, A.M., and Chentsov, A.A., Solving a routing problem with the aid of an independent computations scheme, Bull. South Ural State Univ. Ser. Math. Model. Program. Comput. Software, 2018, vol. 11, no. 1, pp. 60–74. https://doi.org/10.14529/mmp180106
Khachay, M. and Neznakhina, K., Towards tractability of the Euclidean generalized travelling salesman problem in grid clusters defined by a grid of bounded height, Commun. Comput. Inf. Sci., 2018, vol. 871, pp. 68–77. https://link.springer.com/chapter/10.1007/978-3-319-93800-4_6
Chentsov, A., Khachay, M., and Khachay, D., Linear time algorithm for precedence constrained asymmetric generalized traveling salesman problem, IFAC-PapersOnLine, 2016, vol. 49, pp. 651–655. https://doi.org/10.1016/j.ifacol.2016.07.767
Hoeft, J. and Palekar, U., Heuristics for the plate-cutting traveling salesman problem, IIE Trans., 1997, vol. 29, pp. 719–731. https://doi.org/10.1023/A:1018582320737
Dewil, R., Vansteenwegen, P., and Cattrysse, D., Construction heuristics for generating tool paths for laser cutters, Int. J. Prod. Rts., 2014, vol. 52, no. 20, pp. 5965–5984. https://doi.org/10.1080/00207543.2014.895064
Crockford, D., The Application/json Media Type for JavaScript Object Notation (JSON), Internet Engineering Task Force, 2006. https://www.rfc-editor.org/info/rfc4627
Makarovskikh, T.A., Panyukov, A.V., and Savitskiy, E.A., Software for the problem of constructing cutting tool motion path, Tr. XVIII-i Mezhdunar. molodezhnoi konf. “Sistemy proektirovaniya, tekhnologicheskoi podgotovki proizvodstva i upravleniya etapami zhiznennogo tsikla promyshlennogo produkta (CAD/CAM/PDM-2018)” (Proc. XVIII Int. Youth Conf. “Design Systems for Industrial Technological Preparation and Control over Stages of an Industrial Product Lifecycle (CAD/CAM/PDM-2018)”) (2018), pp. 172–176.
Makarovskikh, T.A., Panyukov, A.V., and Savitskiy, E.A., Cutting tool routing problem: software implementation, in Tr. XIII Vseross. soveshchaniya po problemam upravleniya (VSPU-2019) (Proc. XIII All-Russia Meeting on Control Problems (VSPU-2019)) Novikov, D.A., Ed., 2019, pp. 2650–2654.
Makarovskikh, T.A., Panyukov, A.V., and Savitskiy, E.A., Software development for cutting tool routing problems, Procedia Manuf., 2019, vol. 29, pp. 567–574. https://doi.org/10.1016/j.promfg.2019.02.123
Makarovskikh, T.A., Panyukov, A.V., and Savitskiy, E.A., Mathematical models and routing algorithms for economical cutting tool paths, Int. J. Prod. Rts., 2018, vol. 5, no. 3, pp. 1171–1188. https://doi.org/10.1080/00207543.2017.1401746
Manber, U. and Bent, S.W., On non-intersecting Eulerian circuits, Discrete Appl. Math., 1987, vol. 18, pp. 87–94. https://doi.org/10.1016/0166-218X(87)90045-X
Makarovskikh, T.A., Software for constructing A-circuits with ordered enclosing in a plane connected 4-regular graph, Vestn. Yuzhn.-Ural. Gos. Univ. Ser. Vychisl. Mat. Inf., 2019, vol. 8, no. 1, pp. 36–53. https://doi.org/10.14529/cmse190103
Makarovskikh, T.A., Constructing nonintersecting \(OE \)-routes in a plane Eulerian graph, Vestn. Yuzhn.-Ural. Gos. Univ. Ser. Vychisl. Mat. Inf., 2019, vol. 8, no. 4, pp. 30–42. https://doi.org/10.14529/cmse190403
Makarovskikh, T.A., On the number of \(OE \)-trails for a fixed transition system, Vestn. Yuzhn.-Ural.Gos. Univ. Ser. Mat. Mekh. Fiz., 2016, vol. 8, no. 1, pp. 5–12. https://doi.org/10.14529/mmph160101
Garey, M.R. and Johnson, D.S., Computers and Intractability: a Guide to the Theory of NP-Completeness, San Francisco: W.H. Freeman, 1979.
Funding
This work was supported by the RF Government, Act no. 211 of March 16, 2013, Agreement no. 02.A03.21.0011 and by the RF Ministry of Science and Higher Education, State Order no. FENU-2020-0022.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Translated by V. Potapchouck
Rights and permissions
About this article
Cite this article
Makarovskikh, T.A., Panyukov, A.V. Software for the Problem of Constructing Cutting Tool Paths in CAD/CAM Systems for Technological Preparation of Cutting Processes. Autom Remote Control 82, 468–480 (2021). https://doi.org/10.1134/S0005117921030073
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117921030073