Precise algebraic-based swept volumes for arbitrary free-form shaped tools towards multi-axis CNC machining verification

Jinesh Machchhar; Denys Plakhotnik; Gershon Elber

doi:10.1016/j.cad.2017.05.015

Precise algebraic-based swept volumes for arbitrary free-form shaped tools towards multi-axis CNC machining verification

Jinesh Machchhar^*, Denys Plakhotnik, Gershon Elber

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

28 Citations (Scopus)

Abstract

This paper presents an algebraic based approach and a computational framework for the simulation of multi-axis CNC machining of general freeform tools. The boundary of the swept volume of the tool is precisely modeled by a system of algebraic constraints, using B-spline basis functions. Subdivision-based solvers are then employed to solve these equations, resulting in a topologically guaranteed construction of the swept volume. The presented algebraic-based method readily generalizes to accept tools of arbitrary free-form shape as input, and at the same time, delivers high degree of precision. Being a common representation in CNC simulations, the computed swept volume can be reduced to a dexels’ representation. Several multi-axis test cases are exhibited using an implementation of our algorithm, demonstrating the robustness and efficacy of our approach.

Original language	English
Pages (from-to)	48-58
Number of pages	11
Journal	Computer-Aided Design
Volume	90
DOIs	https://doi.org/10.1016/j.cad.2017.05.015
Publication status	Published - 1 Sept 2017
Externally published	Yes

Keywords

Algebraic constraints
B-spline surfaces
Dexel grids
Envelopes
Simulation

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1016/j.cad.2017.05.015

Cite this

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title = "Precise algebraic-based swept volumes for arbitrary free-form shaped tools towards multi-axis CNC machining verification",

abstract = "This paper presents an algebraic based approach and a computational framework for the simulation of multi-axis CNC machining of general freeform tools. The boundary of the swept volume of the tool is precisely modeled by a system of algebraic constraints, using B-spline basis functions. Subdivision-based solvers are then employed to solve these equations, resulting in a topologically guaranteed construction of the swept volume. The presented algebraic-based method readily generalizes to accept tools of arbitrary free-form shape as input, and at the same time, delivers high degree of precision. Being a common representation in CNC simulations, the computed swept volume can be reduced to a dexels{\textquoteright} representation. Several multi-axis test cases are exhibited using an implementation of our algorithm, demonstrating the robustness and efficacy of our approach.",

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author = "Jinesh Machchhar and Denys Plakhotnik and Gershon Elber",

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doi = "10.1016/j.cad.2017.05.015",

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journal = "Computer-Aided Design",

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T1 - Precise algebraic-based swept volumes for arbitrary free-form shaped tools towards multi-axis CNC machining verification

AU - Machchhar, Jinesh

AU - Plakhotnik, Denys

AU - Elber, Gershon

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Y1 - 2017/9/1

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AB - This paper presents an algebraic based approach and a computational framework for the simulation of multi-axis CNC machining of general freeform tools. The boundary of the swept volume of the tool is precisely modeled by a system of algebraic constraints, using B-spline basis functions. Subdivision-based solvers are then employed to solve these equations, resulting in a topologically guaranteed construction of the swept volume. The presented algebraic-based method readily generalizes to accept tools of arbitrary free-form shape as input, and at the same time, delivers high degree of precision. Being a common representation in CNC simulations, the computed swept volume can be reduced to a dexels’ representation. Several multi-axis test cases are exhibited using an implementation of our algorithm, demonstrating the robustness and efficacy of our approach.

KW - Algebraic constraints

KW - B-spline surfaces

KW - Dexel grids

KW - Envelopes

KW - Simulation

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JF - Computer-Aided Design

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Precise algebraic-based swept volumes for arbitrary free-form shaped tools towards multi-axis CNC machining verification

Abstract

Keywords

UN SDGs

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