A real-time look-ahead interpolation methodology with curvature-continuous B-spline transition scheme for CNC machining of short line segments

Straight lines, or G01 blocks, are the most widespread representation form for the tool path in CNC machining. At the junctions between consecutive segments, the tangency and curvature discontinuities may lead to feedrate fluctuation and acceleration oscillation, which would deteriorate the machinin...

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Veröffentlicht in:	International journal of machine tools & manufacture Jg. 65; S. 88 - 98
Hauptverfasser:	Zhao, Huan, Zhu, LiMin, Ding, Han
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Elsevier Ltd 01.02.2013
Schlagworte:	Acceleration Algorithms Analytical curvature extrema B-spline Bidirectional scanning Curvature G2 continuity Machining Mathematical analysis Real time Segments Transition scheme Transition scheme Bidirectional scanning B-spline G2 continuity Analytical curvature extrema
ISSN:	0890-6955, 1879-2170
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Abstract	Straight lines, or G01 blocks, are the most widespread representation form for the tool path in CNC machining. At the junctions between consecutive segments, the tangency and curvature discontinuities may lead to feedrate fluctuation and acceleration oscillation, which would deteriorate the machining efficiency and quality. To solve this problem, a real-time path-smoothing method is proposed, which adopts a curvature-continuous B-spline with five control points to blend the adjacent straight lines. The advantage of the transition scheme is that, G2 continuity, analytical calculation of the curvature extrema, approximation error control and real-time performance are considered simultaneously. Then, a bidirectional scanning algorithm for jerk limited S-shape feedrate profile is proposed to evaluate the feedrate constraints. On this basis, a real-time look-ahead scheme, which comprises of path-smoothing, bidirectional scanning and feedrate scheduling, is developed to acquire a feedrate profile with smooth acceleration. Also, an arc-length based interpolation algorithm for mixed linear and parametric segments is proposed to overcome the difficulty of crossing different segments. With these schemes, the smoothness of both tool path and feedrate is guaranteed. Simulation and experiments on an X–Y–Z platform are conducted. The results demonstrate the feasibility and efficiency of the present algorithms. ► A real-time transition method applying B-splines to blend line segments is proposed. ► G2 continuity, curvature extrema, approximation error are considered simultaneously. ► A bidirectional scanning method is proposed to determine the feedrate constraints. ► A look-ahead scheme is developed to acquire a jerk-limited S-shape feedrate profile. ► An interpolation method for mixed linear and parametric segments is developed.
AbstractList	Straight lines, or G01 blocks, are the most widespread representation form for the tool path in CNC machining. At the junctions between consecutive segments, the tangency and curvature discontinuities may lead to feedrate fluctuation and acceleration oscillation, which would deteriorate the machining efficiency and quality. To solve this problem, a real-time path-smoothing method is proposed, which adopts a curvature-continuous B-spline with five control points to blend the adjacent straight lines. The advantage of the transition scheme is that, G2 continuity, analytical calculation of the curvature extrema, approximation error control and real-time performance are considered simultaneously. Then, a bidirectional scanning algorithm for jerk limited S-shape feedrate profile is proposed to evaluate the feedrate constraints. On this basis, a real-time look-ahead scheme, which comprises of path-smoothing, bidirectional scanning and feedrate scheduling, is developed to acquire a feedrate profile with smooth acceleration. Also, an arc-length based interpolation algorithm for mixed linear and parametric segments is proposed to overcome the difficulty of crossing different segments. With these schemes, the smoothness of both tool path and feedrate is guaranteed. Simulation and experiments on an X–Y–Z platform are conducted. The results demonstrate the feasibility and efficiency of the present algorithms. ► A real-time transition method applying B-splines to blend line segments is proposed. ► G2 continuity, curvature extrema, approximation error are considered simultaneously. ► A bidirectional scanning method is proposed to determine the feedrate constraints. ► A look-ahead scheme is developed to acquire a jerk-limited S-shape feedrate profile. ► An interpolation method for mixed linear and parametric segments is developed. Straight lines, or G01 blocks, are the most widespread representation form for the tool path in CNC machining. At the junctions between consecutive segments, the tangency and curvature discontinuities may lead to feedrate fluctuation and acceleration oscillation, which would deteriorate the machining efficiency and quality. To solve this problem, a real-time path-smoothing method is proposed, which adopts a curvature-continuous B-spline with five control points to blend the adjacent straight lines. The advantage of the transition scheme is that, G2 continuity, analytical calculation of the curvature extrema, approximation error control and real-time performance are considered simultaneously. Then, a bidirectional scanning algorithm for jerk limited S-shape feedrate profile is proposed to evaluate the feedrate constraints. On this basis, a real-time look-ahead scheme, which comprises of path-smoothing, bidirectional scanning and feedrate scheduling, is developed to acquire a feedrate profile with smooth acceleration. Also, an arc-length based interpolation algorithm for mixed linear and parametric segments is proposed to overcome the difficulty of crossing different segments. With these schemes, the smoothness of both tool path and feedrate is guaranteed. Simulation and experiments on an XaYaZ platform are conducted. The results demonstrate the feasibility and efficiency of the present algorithms.
Author	Zhao, Huan Ding, Han Zhu, LiMin
Author_xml	– sequence: 1 givenname: Huan surname: Zhao fullname: Zhao, Huan – sequence: 2 givenname: LiMin surname: Zhu fullname: Zhu, LiMin email: zhulm@sjtu.edu.cn – sequence: 3 givenname: Han surname: Ding fullname: Ding, Han
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Snippet	Straight lines, or G01 blocks, are the most widespread representation form for the tool path in CNC machining. At the junctions between consecutive segments,...
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SubjectTerms	Acceleration Algorithms Analytical curvature extrema B-spline Bidirectional scanning Curvature G2 continuity Machining Mathematical analysis Real time Segments Transition scheme
Title	A real-time look-ahead interpolation methodology with curvature-continuous B-spline transition scheme for CNC machining of short line segments
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