Optimizing tool size and tool path of five-axis flank milling with bounded constraints via normal mapping

Yu, Liang; Zhong, Lei; Wang, Yuhan

doi:10.1177/1687814017724704

“…Optimizing simultaneously both the tool trajectory and its size and/or shape is a very active research area [25,26,27,28,29,30] and our research belongs to this category of algorithms. To the best of our knowledge, all previous research requires the initial milling trajectory as a part of the input or is indicated by the user.…”

Section: Previous Work and Contributionsmentioning

confidence: 99%

5-axis double-flank CNC machining of spiral bevel gears via custom-shaped milling tools — Part I: Modeling and simulation

Bo

¹

,

González

²

,

Calleja

³

et al. 2020

Precision Engineering

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“…The most recent research focuses on custom-shaped tools. That is, not only the 3D motion of the tool, but also the shape itself are the unknowns in path-planning [19,51,52,53,54,55]. Typically, the initial milling trajectory is a part of the input or is indicated by the user.…”

Section: Cnc Machiningmentioning

confidence: 99%

Characterizing envelopes of moving rotational cones and applications in CNC machining

Skopenkov

¹

,

Bo

²

,

Bartoň

³

et al. 2020

Computer Aided Geometric Design

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Motivated by applications in CNC machining, we provide a characterization of surfaces which are enveloped by a oneparametric family of congruent rotational cones. As limit cases, we also address ruled surfaces and their offsets. The characterizations are higher order nonlinear PDEs generalizing the ones by Gauss and Monge for developable surfaces and ruled surfaces, respectively. The derivation includes results on local approximations of a surface by cones of revolution, which are expressed by contact order in the space of planes. To this purpose, the isotropic model of Laguerre geometry is used as there rotational cones correspond to curves (isotropic circles) and higher order contact is computed with respect to the image of the input surface in the isotropic model. Therefore, one studies curve-surface contact that is conceptually simpler than the surface-surface case. We show that, in a generic case, there exist at most six positions of a fixed rotational cone that have third order contact with the input surface. These results are themselves of interest in geometric computing, for example in cutter selection and positioning for flank CNC machining.

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“…The most recent research focuses on custom-shaped tools. That is, not only the 3D motion of the tool, but also the shape itself are the unknowns in path-planning [19,51,52,53,54,55]. Typically, the initial milling trajectory is a part of the input or is indicated by the user.…”

Section: Previous Workmentioning

confidence: 99%

Characterizing envelopes of moving rotational cones and applications in CNC machining

Skopenkov¹,

Bo²,

Bartoň³

et al. 2020

Preprint

0

View full text Add to dashboard Cite

Motivated by applications in CNC machining, we provide a characterization of surfaces which are enveloped by a oneparametric family of congruent rotational cones. As limit cases, we also address developable surfaces and ruled surfaces. The characterizations are higher order nonlinear PDEs generalizing the ones by Gauss and Monge for developable surfaces and ruled surfaces, respectively. The derivation includes results on local approximations of a surface by cones of revolution, which are expressed by contact order in the space of planes. These results are themselves of interest in geometric computing, for example in cutter selection and positioning for flank CNC machining.

show abstract

Optimizing tool size and tool path of five-axis flank milling with bounded constraints via normal mapping

Cited by 6 publications

References 30 publications

5-axis double-flank CNC machining of spiral bevel gears via custom-shaped milling tools — Part I: Modeling and simulation

5-axis double-flank CNC machining of spiral bevel gears via custom-shaped milling tools — Part I: Modeling and simulation

Characterizing envelopes of moving rotational cones and applications in CNC machining

Characterizing envelopes of moving rotational cones and applications in CNC machining

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