Mathematical models and routing algorithms for CAD technological preparation of cutting processes

Makarovskikh, Tatiana; Panyukov, Anatoly V.; Savitskiy, E. A.

doi:10.1134/s0005117917050095

Cited by 7 publications

(5 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Constructing of an OE-route for graph G solves the above stated tool path problem when a part cut of a sheet does not require any further cuts (see constraint (1)). Routes with a minimum number of chains are of the major interest since the transition from one chain to another corresponds to the air move.…”

Section: Oe-routes For Any Plane Graphsmentioning

confidence: 99%

“…OE-Cycle) [19], [21] O(|E| • log 2 |E|) OE-Postman Route (alg. CPP OE) [17] O(|E| • |V |) OE-Router [1] O(|E| • log 2 |E|) Optimal OE-Router [1] O(|V | 2 ) MultiComponent (OE-Cover for Disconnected graph [18]) O(|E| • log 2 |E|) DoubleBridging (OE-Cover for Disconnected graph [18])…”

Section: Route Typementioning

confidence: 99%

“…(1) all elements of the inner contours must be cut before the outer contour is completely covered (OE-chains [1]);…”

Section: Introductionmentioning

confidence: 99%

“…As functions v k (e), f k (e), l k (e), r k (e), k = 1, 2, constructed on graph G = (V, E) edges define incident vertices for each edge, incident faces, and adjacent edges, the following statement holds. Functions v k (e), f k (e), l k (e), r k (e), k = 1, 2 constructed on graph G = (V, E) edges define plane graph G = (V, E) up to homeomorphism [1].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The estimation of the number of OE-chains and realizable OE-routes for cutting plans with combined contours

Makarovskikh

Savitsky

2020

YUGOSLAV J OPERATION

View full text Add to dashboard Cite

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.

show abstract

Section: Oe-routes For Any Plane Graphsmentioning

confidence: 99%

Section: Route Typementioning

confidence: 99%

“…(1) all elements of the inner contours must be cut before the outer contour is completely covered (OE-chains [1]);…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The estimation of the number of OE-chains and realizable OE-routes for cutting plans with combined contours

Makarovskikh

Savitsky

2020

YUGOSLAV J OPERATION

View full text Add to dashboard Cite

show abstract

“…Algorithm FaceCutting [35] is one other way to obtain graph G without bridges. It consists in splitting the separating face using the Hamiltonian cycle.…”

mentioning

confidence: 99%

Special Type Routing Problems in Plane Graphs

Makarovskikh

Panyukov

2022

Mathematics

View full text Add to dashboard Cite

We considered routing problems for plane graphs to solve control problems of cutting machines in the industry. According to the cutting plan, we form its homeomorphic image in the form of a plane graph G. We determine the appropriate type of route for the given graph: OE-route represents an ordered sequence of chains satisfying the requirement that the part of the route that is not passed does not intersect the interior of its passed part, AOE-chain represents OE-chain consecutive edges which are incident to vertex v and they are neighbours in the cyclic order O±(v), NOE-route represents the non-intersecting OE-route, PPOE-route represents the Pierce Point NOE-route with allowable pierce points that are start points of OE-chains forming this route. We analyse the solvability of the listed routing problems in graph G. We developed the polynomial algorithms for obtaining listed routes with the minimum number of covering paths and the minimum length of transitions between the ending of the current path and the beginning of the next path. The solutions proposed in the article can improve the quality of technological preparation of cutting processes in CAD/CAM systems.

show abstract

Software for Constructing A-chains with Ordered Enclosing for a Plane Connected 4-regular Graph

Makarovskikh

Panyukov

2019

IFAC-PapersOnLine

View full text Add to dashboard Cite

Mathematical models and routing algorithms for CAD technological preparation of cutting processes

Cited by 7 publications

References 7 publications

The estimation of the number of OE-chains and realizable OE-routes for cutting plans with combined contours

The estimation of the number of OE-chains and realizable OE-routes for cutting plans with combined contours

Special Type Routing Problems in Plane Graphs

Software for Constructing A-chains with Ordered Enclosing for a Plane Connected 4-regular Graph

Contact Info

Product

Resources

About