The estimation of the number of OE-chains and realizable OE-routes for cutting plans with combined contours
DOI:
https://doi.org/10.2298/YJOR191024025MKeywords:
Ordered Enclosing, Pierce point placement, Enumeration, Routing problem, Cutting, Technological restrictions, Cut realizationAbstract
Cuts combination of plane details leads to optimization of material use and shortening of cutting time. However, the problem of cutting plan realization arises. This plan has to satisfy the following restrictions: (1) part cut off a sheet does not require further cuts (constructing of OE-route); (2) there are some restrictions on placement of pierce points (constructing of PPOE-cover). In this paper we consider the problem of enumeration the OE-chains for cutting plan with combined cuts and necessary conditions of realizable cutting.References
Makarovskikh, T.A., Panyukov, A.V., and Savitsky, E.A., "Mathematical Models and Routing Algorithms for CAD Technological Preparation of Cutting Processes", Automation and Remote Control, 78 (4) (2017) 868-882.
Dewil, R., Vansteenwegen, P., and Cattrysse, D., "A Review of Cutting Path Algorithms for Laser Cutters", International Journal Advanced Manufacturing Technology, 87 (2016) 1865-1884.
Makarovskikh, T., and Panyukov, A., "The Cutter Trajectory Avoiding Intersections of Cuts", IFAC-PapersOnLine, 50 (1) (2017) 2284-2289.
Li, X., Liu, Z., Wang, F., Yi, B., and Song, Y., "Combining physical shell mapping and reverse-compensation optimisation for spiral machining of free-form surfaces", International Journal of Production Research, 57 (13) (2018) 1-14.
Makarovskikh, T., and Panyukov, A., "Development of routing methods for cutting out details", CEUR Workshop Proceedings, 2098 (2018) 249-263.
Dewil, R., Vansteenwegen, P., Cattrysse, D., Laguna, M., and Vossen, T., "An Improvement Heuristic Framework for the Laser Cutting Tool Path Problem", International Journal of Production Research, 53 (6) (2015) 1761-1776.
Petunin, A., and Stylios, C., "Optimization Models of Tool Path Problem for CNC Sheet Metal Cutting Machines", IFAC-PapersOnLine, 49 (2016) 23-28.
Petunin, A., Chentsov, A.G., and Chentsov, P.A., "About routing in the sheet cutting", Bulletin of the South Ural State University, Series: Mathematical Modelling, Programming and Computer Software, 10 (3) (2017) 25-39.
Chentsov, A.G., Grigoryev, A.M., and Chentsov, A.A., "Solving a Routing Problem with the Aid of an Independent Computations Scheme", Bulletin of the South Ural State University, Series: Mathematical Modelling, Programming and Computer Software, 11 (1) (2018) 60-74.
Khachay, M., and Neznakhina, K., "Towards Tractability of the Euclidean Generalized Travelling Salesman Problem in Grid Clusters Defined by a Grid of Bounded Height", Communications in Computer and Information Science, 871 (2018) 68-77.
Chentsov, A., Khachay, M., and Khachay, D., "Linear Time Algorithm for Precedence Constrained Asymmetric Generalized Traveling Salesman Problem", IFAC-PapersOnLine, 49 (2016) 651-655.
Hoeft, J., and Palekar, U., "Heuristics for the Plate-cutting Travelling Salesman Problem", IIE Transactions, 29 (9) (1997) 719-731.
Dewil, R., Vansteenwegen, P., and Cattrysse, D., "Construction heuristics for generating tool paths for laser cutters", International Journal of Production Research, 52 (20) (2014) 5965-5984.
Hajad, M., Tangwarodomnukun, V., Jaturanonda, Ch., and Dumkum, Ch., "Laser cutting path optimization using simulated annealing with an adaptive large neighborhood search", The International Journal of Advanced Manufacturing Technology, 103 (2019) 1-12.
Manber, U., and Israni, S., "Pierce Point Minimization and Optimal Torch Path Determination in Flame Cutting", Journal of Manufacturing Systems, 3 (1) (1984) 81-89.
Garfinkel, R.S., and Webb, I.R., "On crossings, the Crossing Postman Problem, and the Rural Postman Problem", Networks, 34 (3) (1999) 173-180.
Panyukova, T.A., "Constructing of OE-postman Path for a Planar Graph", Bulletin of the South Ural State University, Series: Mathematical Modelling, Programming and Computer Software, 7 (4) (2014) 90-101.
Makarovskikh, T.A., Panyukov, A.V., and Savitskiy, E.A., "Mathematical models and routing algorithms for economical cutting tool paths", International Journal of Production Research, 56 (3) (2018) 1171-1188.
Panyukova, T., "Chain Sequences with Ordered Enclosing", Journal of Computer and System Sciences International, 46 (1) (2007) 83-92.
Panioukova, T.A., and Panyukov, A.V., "Algorithms for Construction of Ordered Enclosing Traces in Planar Eulerian Graphs", Proc. 6th Workshop on Computer Science and Information Technologies CSIT2003, Ula, Russia, 1 (2003) 134-138.
Panyukova, T., "Eulerian Cover with Ordered Enclosing for Flat Graphs", Electronic Notes in Discrete Mathematics, 28 (2007) 17-24.
Makarovskikh, T.A., "On the number of starting points for a fixed cutting plan and fixed cutter trajectory", Proceedings of the 2-nd International Conference Intelligent Technologies for Information Processing and Management, Ula, Russia, 1 (2014) 239-244.
Makarovskikh, T.A., "On the Number of OE-trails for a Fixed Transition System", Bulletin of the South Ural State University, Series: Mathematics Mechanics Physics, 8 (1) (2016) 5-12 (in Russian).
Makarovskikh, T.A., and Panyukov, A.V., "AOE-Trails Constructing for a Plane Connected 4-Regular Graph", CEUR Workshop Proceedings, 1623 (2016) 62-71.
Savitsky, E.A., and Makarovskikh, T.A., "The OE-cover for a plane graph by chains with allowed starting vertices", CEUR Workshop Proceedings, 2064 (2017) 103-111.
Makarovskikh, T., and Panyukov, A., "Development of routing methods for cutting out details", CEUR Workshop Proceedings, 2098 (2018) 249-263.
Makarovskikh, T., Panyukov, A., Savitsky, E., "Software Development for Cutting Tool Routing Problems", Procedia Manufacturing, 29 (2019) 567-574.
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