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- 저자 : Aras Eyyup (검색결과 2 건)
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Tracing sub-surface swept profiles of tapered toroidal end mills between level cuts
Eyyup Aras 한국CDE학회 2019 Journal of computational design and engineering Vol.6 No.4
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 expres-sion in one variable has been deduced using two moving frames. The basic idea behind such a formula-tion 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.
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Vector-valued envelope functions for constructing tool swept surfaces in continuous domains
Aras Eyyup 한국CDE학회 2023 Journal of computational design and engineering Vol.10 No.2
This paper proposes the vector-valued envelope functions to describe form cutters’ swept profiles at the choice of particular motion instances. The general idea behind such a formulation is to embed the tangency constraint into the tool surface expression and form a single continuous function to describe the segmental curves whose elements lie on the envelopes. This results in skipping unnecessary calculations when no envelope-surface point is associated with the specified input data, reducing the sizeable computational burden due to repetitive constraint implementations, and most importantly, depending on the tool kinematics’ complexity, avoiding the tangency-constraint violations between successive envelope-surface points where the exact fit cannot be obtained. In this study, firstly, the NC tool surface models present in extant literature have been restructured using the four-parameter set of spheres to attain the required one-to-one correspondence between the domain and range sets of these functions, followed by excluding the tangency-constraint evaluations by introducing the systematic parameter-reduction procedures that led to the development of constraint-embedded envelope functions. Next, we introduced the branch-existence test, which allowed us to check whether these functions are continuous over closed domain intervals. Finally, we covered algorithms for implementing the functions.
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