On C0 and C1 continuity of envelopes of rotational solids and its application to 5-axis CNC machining

We study the smoothness of envelopes generated by motions of rotational rigid bodies in the context of 5-axis Computer Numerically Controlled (CNC) machining. A moving cutting tool, conceptualized as a rotational solid, forms a surface, called envelope, that delimits a part of 3D space where the too...

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Bibliographic Details
Authors: Ponce Vanegas, F., Bizzarri, M., Barton, M.
Format: article
Status:Versión enviada para evaluación y publicación
Publication Date:2023
Country:España
Institution:Basque Center for Applied Mathematics (BCAM)
Repository:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1638
Online Access:http://hdl.handle.net/20.500.11824/1638
https://doi.org/10.1016/j.cagd.2023.102245
Access Level:Open access
Keyword:motion regularity
C0 tool
envelope
5-axis flank CNC machining
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spelling On C0 and C1 continuity of envelopes of rotational solids and its application to 5-axis CNC machiningPonce Vanegas, F.Bizzarri, M.Barton, M.motion regularityC0 toolenvelope5-axis flank CNC machiningWe study the smoothness of envelopes generated by motions of rotational rigid bodies in the context of 5-axis Computer Numerically Controlled (CNC) machining. A moving cutting tool, conceptualized as a rotational solid, forms a surface, called envelope, that delimits a part of 3D space where the tool engages the material block. The smoothness of the resulting envelope depends both on the smoothness of the motion and smoothness of the tool. While the motions of the tool are typically required to be at least C2, the tools are frequently only C0 continuous, which results in discontinuous envelopes. In this work, we classify a family of instantaneous motions that, in spite of only C0 continuous shape of the tool, result in C0 continuous envelopes. We show that such motions are flexible enough to follow a free-form surface, preserving tangential contact between the tool and surface along two points, therefore having applications in shape slot milling or in a semi-finishing stage of 5-axis flank machining. We also show that C1 tools and motions still can generate smooth envelopes.Juan de la Cierva - Formation [grant number FJC2019-039804-I] Ram\ón y Cajal fellowship RYC-2017-22649.202320232023info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/1638https://doi.org/10.1016/j.cagd.2023.102245reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Inglésinfo:eu-repo/grantAgreement/EC/H2020/862025info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-104488RB-I00info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2021-122156NB-I00info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2022-2025Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/16382026-06-19T12:47:47Z
dc.title.none.fl_str_mv On C0 and C1 continuity of envelopes of rotational solids and its application to 5-axis CNC machining
title On C0 and C1 continuity of envelopes of rotational solids and its application to 5-axis CNC machining
spellingShingle On C0 and C1 continuity of envelopes of rotational solids and its application to 5-axis CNC machining
Ponce Vanegas, F.
motion regularity
C0 tool
envelope
5-axis flank CNC machining
title_short On C0 and C1 continuity of envelopes of rotational solids and its application to 5-axis CNC machining
title_full On C0 and C1 continuity of envelopes of rotational solids and its application to 5-axis CNC machining
title_fullStr On C0 and C1 continuity of envelopes of rotational solids and its application to 5-axis CNC machining
title_full_unstemmed On C0 and C1 continuity of envelopes of rotational solids and its application to 5-axis CNC machining
title_sort On C0 and C1 continuity of envelopes of rotational solids and its application to 5-axis CNC machining
dc.creator.none.fl_str_mv Ponce Vanegas, F.
Bizzarri, M.
Barton, M.
author Ponce Vanegas, F.
author_facet Ponce Vanegas, F.
Bizzarri, M.
Barton, M.
author_role author
author2 Bizzarri, M.
Barton, M.
author2_role author
author
dc.subject.none.fl_str_mv motion regularity
C0 tool
envelope
5-axis flank CNC machining
topic motion regularity
C0 tool
envelope
5-axis flank CNC machining
description We study the smoothness of envelopes generated by motions of rotational rigid bodies in the context of 5-axis Computer Numerically Controlled (CNC) machining. A moving cutting tool, conceptualized as a rotational solid, forms a surface, called envelope, that delimits a part of 3D space where the tool engages the material block. The smoothness of the resulting envelope depends both on the smoothness of the motion and smoothness of the tool. While the motions of the tool are typically required to be at least C2, the tools are frequently only C0 continuous, which results in discontinuous envelopes. In this work, we classify a family of instantaneous motions that, in spite of only C0 continuous shape of the tool, result in C0 continuous envelopes. We show that such motions are flexible enough to follow a free-form surface, preserving tangential contact between the tool and surface along two points, therefore having applications in shape slot milling or in a semi-finishing stage of 5-axis flank machining. We also show that C1 tools and motions still can generate smooth envelopes.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023
2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/1638
https://doi.org/10.1016/j.cagd.2023.102245
url http://hdl.handle.net/20.500.11824/1638
https://doi.org/10.1016/j.cagd.2023.102245
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/EC/H2020/862025
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-104488RB-I00
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2021-122156NB-I00
info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2022-2025
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
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dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
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