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Tracing sub-surface swept profiles of tapered toroidal end mills between level cuts
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| Zeitschriftentitel: | Journal of Computational Design and Engineering |
|---|---|
| Personen und Körperschaften: | |
| In: | Journal of Computational Design and Engineering, 6, 2019, 4, S. 629-646 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
Oxford University Press (OUP)
|
| Schlagwörter: |
| author_facet |
Aras, Eyyup Aras, Eyyup |
|---|---|
| author |
Aras, Eyyup |
| spellingShingle |
Aras, Eyyup Journal of Computational Design and Engineering Tracing sub-surface swept profiles of tapered toroidal end mills between level cuts Computational Mathematics Computer Graphics and Computer-Aided Design Human-Computer Interaction Engineering (miscellaneous) Modeling and Simulation Computational Mechanics |
| author_sort |
aras, eyyup |
| spelling |
Aras, Eyyup 2288-5048 Oxford University Press (OUP) Computational Mathematics Computer Graphics and Computer-Aided Design Human-Computer Interaction Engineering (miscellaneous) Modeling and Simulation Computational Mechanics http://dx.doi.org/10.1016/j.jcde.2019.04.003 <jats:title>Abstract</jats:title> <jats:p>Development of closed-form solutions and algorithms for constructing sub-surface swept profiles (SWP) of toroidal and conical bodies is presented in this paper. While the problem of identifying the entire SWP of such surfaces has been extensively investigated in extant studies, construction of subsurface SWPs has rarely been addressed despite the subject being of great significance to machining process employing nonstandard-shaped NC tools. Torus shapes considered in extant literature are restricted to the fourth quadrant of a tube cross section. In industrial applications, however, profile cutters contain different regions of a toroidal surface. To identify SWP elements in the proposed study, a single analytical expression in one variable has been deduced using two moving frames. The basic idea behind such a formulation is to employ the one-to-many strategy, which greatly reduces the computational cost and effort. Algorithms to identify feasible domains of SWP parameters at each level cut, where toroidal and conical surfaces meet, have also been proposed in this study. This is important, since cutting a tool surfaces along the rotation axis divides SWP-parameter domains into non overlapping sets of intervals that must be addressed for each tool posture. In addition, this study demonstrates that for certain tool postures, while C1 continuity between sub-surfaces is satisfied, the SWP connectivity is lost at some points. To locate these so called singular-characteristic points, some precomputation steps have been performed. Lastly, several factors affecting the smoothness of SWPs have been identified and discussed.</jats:p> <jats:p>Highlights Closed form solutions have been derived for constructing the sub-swept profiles of toroidal tools. Three algorithms have been presented to identify the feasible domains of swept profile parameters. In order to locate the singular-characteristic points some precomputation steps have been carried out. Finally, several factors, affecting the smoothness of the swept profiles, have been identified.</jats:p> Tracing sub-surface swept profiles of tapered toroidal end mills between level cuts Journal of Computational Design and Engineering |
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| title |
Tracing sub-surface swept profiles of tapered toroidal end mills between level cuts |
| title_unstemmed |
Tracing sub-surface swept profiles of tapered toroidal end mills between level cuts |
| title_full |
Tracing sub-surface swept profiles of tapered toroidal end mills between level cuts |
| title_fullStr |
Tracing sub-surface swept profiles of tapered toroidal end mills between level cuts |
| title_full_unstemmed |
Tracing sub-surface swept profiles of tapered toroidal end mills between level cuts |
| title_short |
Tracing sub-surface swept profiles of tapered toroidal end mills between level cuts |
| title_sort |
tracing sub-surface swept profiles of tapered toroidal end mills between level cuts |
| topic |
Computational Mathematics Computer Graphics and Computer-Aided Design Human-Computer Interaction Engineering (miscellaneous) Modeling and Simulation Computational Mechanics |
| url |
http://dx.doi.org/10.1016/j.jcde.2019.04.003 |
| publishDate |
2019 |
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629-646 |
| description |
<jats:title>Abstract</jats:title>
<jats:p>Development of closed-form solutions and algorithms for constructing sub-surface swept profiles (SWP) of toroidal and conical bodies is presented in this paper. While the problem of identifying the entire SWP of such surfaces has been extensively investigated in extant studies, construction of subsurface SWPs has rarely been addressed despite the subject being of great significance to machining process employing nonstandard-shaped NC tools. Torus shapes considered in extant literature are restricted to the fourth quadrant of a tube cross section. In industrial applications, however, profile cutters contain different regions of a toroidal surface. To identify SWP elements in the proposed study, a single analytical expression in one variable has been deduced using two moving frames. The basic idea behind such a formulation is to employ the one-to-many strategy, which greatly reduces the computational cost and effort. Algorithms to identify feasible domains of SWP parameters at each level cut, where toroidal and conical surfaces meet, have also been proposed in this study. This is important, since cutting a tool surfaces along the rotation axis divides SWP-parameter domains into non overlapping sets of intervals that must be addressed for each tool posture. In addition, this study demonstrates that for certain tool postures, while C1 continuity between sub-surfaces is satisfied, the SWP connectivity is lost at some points. To locate these so called singular-characteristic points, some precomputation steps have been performed. Lastly, several factors affecting the smoothness of SWPs have been identified and discussed.</jats:p>
<jats:p>Highlights Closed form solutions have been derived for constructing the sub-swept profiles of toroidal tools. Three algorithms have been presented to identify the feasible domains of swept profile parameters. In order to locate the singular-characteristic points some precomputation steps have been carried out. Finally, several factors, affecting the smoothness of the swept profiles, have been identified.</jats:p> |
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| description | <jats:title>Abstract</jats:title> <jats:p>Development of closed-form solutions and algorithms for constructing sub-surface swept profiles (SWP) of toroidal and conical bodies is presented in this paper. While the problem of identifying the entire SWP of such surfaces has been extensively investigated in extant studies, construction of subsurface SWPs has rarely been addressed despite the subject being of great significance to machining process employing nonstandard-shaped NC tools. Torus shapes considered in extant literature are restricted to the fourth quadrant of a tube cross section. In industrial applications, however, profile cutters contain different regions of a toroidal surface. To identify SWP elements in the proposed study, a single analytical expression in one variable has been deduced using two moving frames. The basic idea behind such a formulation is to employ the one-to-many strategy, which greatly reduces the computational cost and effort. Algorithms to identify feasible domains of SWP parameters at each level cut, where toroidal and conical surfaces meet, have also been proposed in this study. This is important, since cutting a tool surfaces along the rotation axis divides SWP-parameter domains into non overlapping sets of intervals that must be addressed for each tool posture. In addition, this study demonstrates that for certain tool postures, while C1 continuity between sub-surfaces is satisfied, the SWP connectivity is lost at some points. To locate these so called singular-characteristic points, some precomputation steps have been performed. Lastly, several factors affecting the smoothness of SWPs have been identified and discussed.</jats:p> <jats:p>Highlights Closed form solutions have been derived for constructing the sub-swept profiles of toroidal tools. Three algorithms have been presented to identify the feasible domains of swept profile parameters. In order to locate the singular-characteristic points some precomputation steps have been carried out. Finally, several factors, affecting the smoothness of the swept profiles, have been identified.</jats:p> |
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| spelling | Aras, Eyyup 2288-5048 Oxford University Press (OUP) Computational Mathematics Computer Graphics and Computer-Aided Design Human-Computer Interaction Engineering (miscellaneous) Modeling and Simulation Computational Mechanics http://dx.doi.org/10.1016/j.jcde.2019.04.003 <jats:title>Abstract</jats:title> <jats:p>Development of closed-form solutions and algorithms for constructing sub-surface swept profiles (SWP) of toroidal and conical bodies is presented in this paper. While the problem of identifying the entire SWP of such surfaces has been extensively investigated in extant studies, construction of subsurface SWPs has rarely been addressed despite the subject being of great significance to machining process employing nonstandard-shaped NC tools. Torus shapes considered in extant literature are restricted to the fourth quadrant of a tube cross section. In industrial applications, however, profile cutters contain different regions of a toroidal surface. To identify SWP elements in the proposed study, a single analytical expression in one variable has been deduced using two moving frames. The basic idea behind such a formulation is to employ the one-to-many strategy, which greatly reduces the computational cost and effort. Algorithms to identify feasible domains of SWP parameters at each level cut, where toroidal and conical surfaces meet, have also been proposed in this study. This is important, since cutting a tool surfaces along the rotation axis divides SWP-parameter domains into non overlapping sets of intervals that must be addressed for each tool posture. In addition, this study demonstrates that for certain tool postures, while C1 continuity between sub-surfaces is satisfied, the SWP connectivity is lost at some points. To locate these so called singular-characteristic points, some precomputation steps have been performed. Lastly, several factors affecting the smoothness of SWPs have been identified and discussed.</jats:p> <jats:p>Highlights Closed form solutions have been derived for constructing the sub-swept profiles of toroidal tools. Three algorithms have been presented to identify the feasible domains of swept profile parameters. In order to locate the singular-characteristic points some precomputation steps have been carried out. Finally, several factors, affecting the smoothness of the swept profiles, have been identified.</jats:p> Tracing sub-surface swept profiles of tapered toroidal end mills between level cuts Journal of Computational Design and Engineering |
| spellingShingle | Aras, Eyyup, Journal of Computational Design and Engineering, Tracing sub-surface swept profiles of tapered toroidal end mills between level cuts, Computational Mathematics, Computer Graphics and Computer-Aided Design, Human-Computer Interaction, Engineering (miscellaneous), Modeling and Simulation, Computational Mechanics |
| title | Tracing sub-surface swept profiles of tapered toroidal end mills between level cuts |
| title_full | Tracing sub-surface swept profiles of tapered toroidal end mills between level cuts |
| title_fullStr | Tracing sub-surface swept profiles of tapered toroidal end mills between level cuts |
| title_full_unstemmed | Tracing sub-surface swept profiles of tapered toroidal end mills between level cuts |
| title_short | Tracing sub-surface swept profiles of tapered toroidal end mills between level cuts |
| title_sort | tracing sub-surface swept profiles of tapered toroidal end mills between level cuts |
| title_unstemmed | Tracing sub-surface swept profiles of tapered toroidal end mills between level cuts |
| topic | Computational Mathematics, Computer Graphics and Computer-Aided Design, Human-Computer Interaction, Engineering (miscellaneous), Modeling and Simulation, Computational Mechanics |
| url | http://dx.doi.org/10.1016/j.jcde.2019.04.003 |