Accessibility for Line-Cutting in Freeform Surfaces

Sosin, Boris van; Bartoň, Michael; Elber, Gershon

doi:10.1016/j.cad.2019.05.014

Cited by 14 publications

(6 citation statements)

References 34 publications

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“…Computing C−obstacles for arbitrary shapes can be challenging, depending on the choice of representation. For 5-axis machining applications, one of the six DOF for rotation around the tool axis is deemed redundant and the problem is simplified by assuming simple shapes for the rotating tool's closure such as a flat/ball-end cylinders, approximating reachability by visibility, and so on [34][35][36][37][38][39][40][41]. However, the computations can be dramatically simplified by sampling-based approximations [42].…”

Section: Related Workmentioning

confidence: 99%

Topology optimization with accessibility constraint for multi-axis machining

Mirzendehdel

Behandish

Nelaturi

2020

Computer-Aided Design

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In this paper, we present a topology optimization (TO) framework to enable automated design of mechanical components while ensuring the result can be manufactured using multi-axis machining. Although TO improves the part's performance, the as-designed model is often geometrically too complex to be machined and the as-manufactured model can significantly vary due to machining constraints that are not accounted for during TO. In other words, many of the optimized design features cannot be accessed by a machine tool without colliding with the part (or fixtures). The subsequent post-processing to make the part machinable with the given setup requires trial-and-error without guarantees on preserving the optimized performance. Our proposed approach is based on the well-established accessibility analysis formulation using convolutions in configuration space that is extensively used in spatial planning and robotics. We define an inaccessibility measure field (IMF) over the design domain to identify non-manufacturable features and quantify their contribution to non-manufacturability. The IMF is used to penalize the sensitivity field of performance objectives and constraints to prevent formation of inaccessible regions. Unlike existing discrete formulations, our IMF provides a continuous spatial field that is desirable for TO convergence. Our approach applies to arbitrary geometric complexity of the part, tools, and fixtures, and is highly parallelizable on multi-core architecture. We demonstrate the effectiveness of our framework on benchmark and realistic examples in 2D and 3D. We also show that it is possible to directly construct manufacturing plans for the optimized designs based on the accessibility information.

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Section: Related Workmentioning

confidence: 99%

Topology optimization with accessibility constraint for multi-axis machining

Mirzendehdel

Behandish

Nelaturi

2020

Computer-Aided Design

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“…Another class of relevant research deals with the approximation of general free-form (NURBS) surfaces by ruled surfaces [20,44], or even developable surfaces [34,35,39,41,42]. For simple geometries, the process of approximation can be even interactive, while the design of very complex shapes requires many rounds of optimization and is still beyond real-time performance [42].…”

Section: Previous Workmentioning

confidence: 99%

Characterizing envelopes of moving rotational cones and applications in CNC machining

Skopenkov¹,

Bo²,

Bartoň³

et al. 2020

Preprint

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Motivated by applications in CNC machining, we provide a characterization of surfaces which are enveloped by a oneparametric family of congruent rotational cones. As limit cases, we also address developable surfaces and ruled surfaces. The characterizations are higher order nonlinear PDEs generalizing the ones by Gauss and Monge for developable surfaces and ruled surfaces, respectively. The derivation includes results on local approximations of a surface by cones of revolution, which are expressed by contact order in the space of planes. These results are themselves of interest in geometric computing, for example in cutter selection and positioning for flank CNC machining.

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“…[10] studied the algorithm for cutting polyhedral shapes with a hot wire cutter, utilizing computational geometry techniques to solve the problems of lines and segments in the cutting process. Particularly used in recent years when fabricating freeform geometries, in order to find collision-free tangential cutting directions, a conservative algorithm for line cutting with a wire cutter was presented by [11], which provided advanced techniques to remove large amounts of material. Exploring the material cutting of 2D or 3D geometric shapes, in [12], an approximation algorithm for cutting out convex polygons was presented, which can cut convex polygons from the plane at a minimum cost by designing an optimal cutting sequence.…”

Section: Introductionmentioning

confidence: 99%

“…Despite some of the new algorithms and analysis methods being investigated in [11,14], to the best of our knowledge, the theoretical research available on the optimization strategies of block sawing with a circular saw blade for special-shaped stone in the rough machining stage is currently sparse. This is due to the need to touch upon the convex polyhedron (CPH) reconstruction techniques of computational geometry and computer graphics, and the constraints of cutter head feeding along a straight line in the cutting process.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Material Removal Optimization Strategy of 3D Block Cutting Based on Geometric Computation Method

Shao

Liu

2022

Processes

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During the material removal stage in stone rough processing, milling type has been widely explored, which, however, may cause time and material consumption, as well as substantial stress for the environment. To improve the material removal rate and waste reuse rate in the rough processing stage for three-dimensional stone products with a special shape, in this paper, circular saw disc cutting is explored to cut a convex polyhedron out of a blank box, which approaches a target product. Unlike milling optimization, this problem cannot be well solved by mathematical methods, which have to be solved by geometrical methods instead. An automatic block cutting strategy is proposed intuitively by considering a series of geometrical optimization approaches for the first time. To obtain a big removal block, constructing cutting planes based on convex vertices is uniquely proposed. Specifically, the removal vertices (the maximum thickness of material removal) are searched based on the octree algorithm, and the cutting plane is constructed based on this thickness to guarantee a relatively big removal block. Moreover, to minimize the cutting time, the geometrical characteristics of the intersecting convex polygon of the cutting plane with the convex polyhedron are analyzed, accompanied by the constraints of the guillotine cutting mode. The optimization algorithm determining the cutting path is presented with a feed direction accompanied by the shortest cutting stroke, which confirms the shortest cutting time. From the big removal block and shortest cutting time, the suboptimal solution of the average material removal rate (the ratio of material removal volume to cutting time) is generated. Finally, the simulation is carried out on a blank box to approach a bounding sphere both on MATLAB and the Vericut platform. In this case study, for the removal of 85% of material with 19 cuts, the proposed cutting strategy achieves five times higher the average material removal rate than that of one higher milling capacity case.

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Accessibility for Line-Cutting in Freeform Surfaces

Cited by 14 publications

References 34 publications

Topology optimization with accessibility constraint for multi-axis machining

Topology optimization with accessibility constraint for multi-axis machining

Characterizing envelopes of moving rotational cones and applications in CNC machining

Material Removal Optimization Strategy of 3D Block Cutting Based on Geometric Computation Method

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