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Research Papers

Adaptive NC Path Generation From Massive Point Data With Bounded Error

[+] Author and Article Information
Dongdong Zhang, Pinghai Yang

Department of Mechanical, Materials and Aerospace Engineering, Illinois Institute of Technology, Chicago, IL 60616

Xiaoping Qian1

Department of Mechanical, Materials and Aerospace Engineering, Illinois Institute of Technology, Chicago, IL 60616qian@iit.edu

1

Corresponding author.

J. Manuf. Sci. Eng 131(1), 011001 (Dec 04, 2008) (13 pages) doi:10.1115/1.3010710 History: Received April 28, 2008; Revised August 29, 2008; Published December 04, 2008

This paper presents an approach for generating curvature-adaptive finishing tool paths with bounded error directly from massive point data in three-axis computer numerical control (CNC) milling. This approach uses the moving least-squares (MLS) surface as the underlying surface representation. A closed-form formula for normal curvature computation is derived from the implicit form of MLS surfaces. It enables the generation of curvature-adaptive tool paths from massive point data that is critical for balancing the trade-off between machining accuracy and speed. To ensure the path accuracy and robustness for arbitrary surfaces where there might be an abrupt curvature change, a novel guidance field algorithm is introduced. It overcomes potential excessive locality of curvature-adaptive paths by examining the neighboring points’ curvature within a self-updating search bound. Our results affirm that the combination of curvature-adaptive path generation and the guidance field algorithm produces high-quality numerical control (NC) paths from a variety of point cloud data with bounded error.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 4

Surface normal and curve normal. The dense points stand for the input data. The curve is the CC path and points on the CC path are the CC points. The dashed arrows represent the surface normal vectors of the CC points, and the solid ones stand for the curve normal vectors of the CC points.

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Figure 5

Algorithm for sampling guidance points. (a) Display of guidance points in 3D; (b) guidance points on the drive plane; and (c) zoom-in of the frame in (b). The points stand for the input point data, and the crosses represent the guidance points. The forks are the intermediate points used to generate guidance points.

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Figure 9

Curvature-adaptive path generation on the human face: (a) forward normal curvature display; (b) top-view of CC paths (parallel lines) with CC points; (c) isoview of input data and three drive planes; (d) 2D contour on the plane Y=50 mm; (e) 2D contour on the plane Y=85 mm; and (f) 2D contour on the plane Y=120 mm

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Figure 10

Self-updating search bound in the guidance field algorithm: (a) display of the bound self-updating process and (b) zoom-in of the frame in (a)

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Figure 11

Curvature-adaptive tool path intervals of the human face: (a) CC path generation from point data and (b) display of the side normal curvature and adaptive tool path intervals

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Figure 12

Actual NC machining results: (a) semifinishing machining result: the machining tolerance is 0.2 mm and the cusp height is 0.3 mm; (b) finishing machining result: the tolerance and cusp height are 0.1 mm; (c) right-view of the semifinishing machining result; and (d) left-view of the finishing machining result

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Figure 1

CC points, CC paths, and drive planes

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Figure 2

Machining error: (a) tolerance τ: R is the normal curvature in the forward direction and λcc is the forward step; and (b) cusp height η: R′ is the normal curvature in the side direction and ℓcc is the side step

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Figure 3

Guidance field algorithm overcoming the excessive locality of the curvature effect: (a) abrupt changes of the curvature at point A leads to the next CC point at B′ resulting in the path bias; and (b) the guidance field algorithm checks the curvature in the front region and shrinks the forward step accordingly

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Figure 6

Curvature-adaptive 2D contour generation on the compound surface: (a) forward normal curvature display; (b) top-view of CC paths (parallel lines) with CC points; (c) isoview of input data and three drive planes; (d) 2D contour on the plane Y=28 mm; (e) 2D contour on the plane Y=60 mm; and (f) 2D contour on the plane Y=90 mm

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Figure 7

Curvature-adaptive tool path intervals of the compound surface: (a) CC paths generated from point data and (b) display of the side normal curvature and adaptive tool path intervals. Dashed rectangles stand for the regions with a high slope in the side direction.

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Figure 8

Data smoothing from the MLS surface: (a) input data with noise (σ=0.6); (b) points after projecting onto MLS surface; (c) overlap of input data and the projected points; and (d) zoom-in of the frame in (c)

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