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

Technion - Israel Institute of Technology

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

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
State	Published - Sep 2017

Keywords

Algebraic constraints
B-spline surfaces
Dexel grids
Envelopes
Simulation

All Science Journal Classification (ASJC) codes

Computer Science Applications
Computer Graphics and Computer-Aided Design
Industrial and Manufacturing Engineering

UN SDGs

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

Access to Document

10.1016/j.cad.2017.05.015

Cite this

@article{761a1874aafe4fe68ae992c5107e5397,

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.",

keywords = "Algebraic constraints, B-spline surfaces, Dexel grids, Envelopes, Simulation",

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

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Ltd",

year = "2017",

month = sep,

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

language = "الإنجليزيّة",

volume = "90",

pages = "48--58",

journal = "Computer-Aided Design",

issn = "0010-4485",

publisher = "Elsevier Ltd.",

}

TY - JOUR

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

PY - 2017/9

Y1 - 2017/9

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=85019660338&partnerID=8YFLogxK

U2 - 10.1016/j.cad.2017.05.015

DO - 10.1016/j.cad.2017.05.015

M3 - مقالة

SN - 0010-4485

VL - 90

SP - 48

EP - 58

JO - Computer-Aided Design

JF - Computer-Aided Design

ER -

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

UN SDGs

Access to Document

Other files and links

Fingerprint

Cite this