Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2205.11805

Hybrid Manufacturing Process Planning for Arbitrary Part and Tool Shapes

George P. Harabin·Morad Behandish
View original source ↗Read source document ↗Export metadata ↓

Abstract

Hybrid manufacturing (HM) technologies combine additive and subtractive manufacturing (AM/SM) capabilities in multi-modal process plans that leverage the strengths of each. Despite the growing interest in HM technologies, software tools for process planning have not caught up with advances in hardware and typically impose restrictions that limit the design and manufacturing engineers' ability to systematically explore the full design and process planning spaces. We present a general framework for identifying AM/SM actions that make up an HM process plan based on accessibility and support requirements, using morphological operations that allow for arbitrary part and tool geometries to be considered. To take advantage of multi-modality, we define the actions to allow for temporary excessive material deposition or removal, with an understanding that subsequent actions can correct for them, unlike the case in unimodal (AM-only or SM-only) process plans that are monotonic. We use this framework to generate a combinatorial space of valid, potentially non-monotonic, process plans for a given part of arbitrary shape, a collection of AM/SM tools of arbitrary shapes, and a set of relative rotations (fixed for each action) between them, representing build/fixturing directions on $3-$axis machines. Finally, we use define a simple objective function quantifying the cost of materials and operating time in terms of deposition/removal volumes and use a search algorithm to explore the exponentially large space of valid process plans to find "cost-optimal" solutions. We demonstrate the effectiveness of our method on 3D examples.

Explore related subjects

cs.CGcs.AIcs.CEcs.RO

Keep this discovery

BibTeXRIS

George P. Harabin, Morad Behandish. 2022-05-24. Hybrid Manufacturing Process Planning for Arbitrary Part and Tool Shapes. https://doi.org/10.1016/j.cad.2022.103299

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Almost Linear Universal Point Sets for Planar Graphs

A point set is universal for planar graphs on $n$ vertices if every such graph has a straight-line drawing without crossings whose vertices belong to the set. We construct universal point sets of size $n^{1+o(1)}$, improving the previous quadratic upper bound. Our construction uses the reduction of Bannister, Cheng, Devanny, and Eppstein from universal point sets to superpatterns for $213$-avoiding permutations. We represent these permutations by ordered rooted forests and construct a small family of intervals containing every such forest. The result follows from a straightforward bound on the size of the family of intervals. GPT-6 Astra assisted in developing the construction and proof.

cs.CG↗
arXiv2026

Some results on Archdeacon's conjecture for rotation systems

A rotation system on $n$ elements assigns to each element a cyclic order of the other $n-1$ elements. A four-element subset is non-planar if its induced rotation system cannot be realized by a crossing-free drawing of $K_4$. As a combinatorial strengthening of Hill's conjecture on the crossing number of the complete graph, Archdeacon conjectured that every rotation system on $n$ elements has at least $H(n)=\frac{1}{4} \lfloor\frac {n}{2}\rfloor \lfloor\frac{n-1}{2}\rfloor \lfloor\frac{n-2}{2}\rfloor \lfloor\frac{n-3}{2}\rfloor$ non-planar four-element subsets. We computationally verify Archdeacon's conjecture for $n\leq 10$ and show that every extremal rotation system in these orders is realizable by a simple drawing. With computer assistance, we prove that every rotation system on $n$ elements has at least $(8/9 - o(1)) H(n)$ non-planar four-element subsets. We also present a proof by hand for a weaker lower bound of $(2/3-o(1)) H(n)$. Finally, extending recent work of Felsner on antipodal pairs in drawings, we show that Archdeacon's conjecture holds for antipodally shellable rotation systems.

cs.CG↗
arXiv2026

The Hyperbolic Surface Distance, Diameter, and Dirichlet Problems

Despite the prominence of hyperbolic surfaces in mathematics, basic algorithmic questions about them, even computing the distance between two points, have remained open, leaving many features of these surfaces inaccessible. The classical machinery assumes a polyhedral structure absent on a smooth surface. We remove these obstacles. We begin with an efficient $O(g^2)$ algorithm for the distance between two points, where $g$ is the genus of the surface. Building on it, we obtain an $O(g^2 \log g)$ method for answering distance queries from a fixed source and, as a consequence, for recentering a Dirichlet domain around an arbitrary point. This understanding of distances on the surface then lets us approximate the diameter to within any $\eps$ in time $O(g^3 \log g / \eps^2)$. We further show that the diameter, a single real number encoding a great deal about the surface, is exactly computable. Its hyperbolic cosine is an algebraic number over the field encoding the coefficients of the hyperbolic isometries defining the surface.

cs.CG↗