Precise algebraic-based swept volumes for arbitrary free-form shaped tools towards multi-axis CNC machining verification
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-...
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| Veröffentlicht in: | Computer aided design 2017-09, Vol.90, p.48-58 |
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| creator | Machchhar, Jinesh Plakhotnik, Denys Elber, Gershon |
| description | 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.
•A computational framework for multi-axis CNC machining simulation is proposed.•Algebraic modeling of the swept volume of the cutter leads to high precision.•Topological guarantees are given regarding correctness of the solution.•Dexel-grid representation of the swept volume yields computational efficiency.
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| doi_str_mv | 10.1016/j.cad.2017.05.015 |
| format | Article |
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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.
•A computational framework for multi-axis CNC machining simulation is proposed.•Algebraic modeling of the swept volume of the cutter leads to high precision.•Topological guarantees are given regarding correctness of the solution.•Dexel-grid representation of the swept volume yields computational efficiency.
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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.
•A computational framework for multi-axis CNC machining simulation is proposed.•Algebraic modeling of the swept volume of the cutter leads to high precision.•Topological guarantees are given regarding correctness of the solution.•Dexel-grid representation of the swept volume yields computational efficiency.
[Display omitted]</description><subject>Algebra</subject><subject>Algebraic constraints</subject><subject>Algorithms</subject><subject>B-spline surfaces</subject><subject>Basis functions</subject><subject>Computer simulation</subject><subject>Dexel grids</subject><subject>Envelopes</subject><subject>Machining</subject><subject>Numerical controls</subject><subject>Program verification (computers)</subject><subject>Simulation</subject><subject>Solvers</subject><subject>Swept volumes</subject><issn>0010-4485</issn><issn>1879-2685</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp9kE9LxDAQxYMouK5-AG8Bz62ZblITPMniPxD1oOeQJhPN0jZr0l312xtZz15mYHhv5s2PkFNgNTBoz1e1Na5uGFzUTNQMxB6ZgbxQVdNKsU9mjAGrOJfikBzlvGKMNbBQM_L1nNCGjNT0b9glE2zVmYyO5k9cT3Qb-82AmfqYqEldmJJJ39QnxKqMBprfzbqIpxj7XOqnSS7TYdNPoTJfIdPl45IOxr6HMYxvdIsp-GDNFOJ4TA686TOe_PU5eb25flneVQ9Pt_fLq4fKLlo5Va3gSnnuWw9gEbly0psOm1Z10ndcKMGYdK6FhQXmDQjnBHKuAETXWNEs5uRst3ed4scG86RXcZPGclKD4tAqJaUsKtipbIo5J_R6ncJQftXA9C9gvdIFsP4FrJnQBXDxXO48WOJvAyadbcDRoguF6aRdDP-4fwCPfYUy</recordid><startdate>201709</startdate><enddate>201709</enddate><creator>Machchhar, Jinesh</creator><creator>Plakhotnik, Denys</creator><creator>Elber, Gershon</creator><general>Elsevier Ltd</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>F28</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>201709</creationdate><title>Precise algebraic-based swept volumes for arbitrary free-form shaped tools towards multi-axis CNC machining verification</title><author>Machchhar, Jinesh ; Plakhotnik, Denys ; Elber, Gershon</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c368t-65499f4f6f11cee49d8fabe269b8fb4595008dd613c10fa15dd5e449115b2c523</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Algebra</topic><topic>Algebraic constraints</topic><topic>Algorithms</topic><topic>B-spline surfaces</topic><topic>Basis functions</topic><topic>Computer simulation</topic><topic>Dexel grids</topic><topic>Envelopes</topic><topic>Machining</topic><topic>Numerical controls</topic><topic>Program verification (computers)</topic><topic>Simulation</topic><topic>Solvers</topic><topic>Swept volumes</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Machchhar, Jinesh</creatorcontrib><creatorcontrib>Plakhotnik, Denys</creatorcontrib><creatorcontrib>Elber, Gershon</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Computer aided design</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Machchhar, Jinesh</au><au>Plakhotnik, Denys</au><au>Elber, Gershon</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Precise algebraic-based swept volumes for arbitrary free-form shaped tools towards multi-axis CNC machining verification</atitle><jtitle>Computer aided design</jtitle><date>2017-09</date><risdate>2017</risdate><volume>90</volume><spage>48</spage><epage>58</epage><pages>48-58</pages><issn>0010-4485</issn><eissn>1879-2685</eissn><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.
•A computational framework for multi-axis CNC machining simulation is proposed.•Algebraic modeling of the swept volume of the cutter leads to high precision.•Topological guarantees are given regarding correctness of the solution.•Dexel-grid representation of the swept volume yields computational efficiency.
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| language | eng |
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| source | ScienceDirect Journals (5 years ago - present) |
| subjects | Algebra Algebraic constraints Algorithms B-spline surfaces Basis functions Computer simulation Dexel grids Envelopes Machining Numerical controls Program verification (computers) Simulation Solvers Swept volumes |
| title | Precise algebraic-based swept volumes for arbitrary free-form shaped tools towards multi-axis CNC machining verification |
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