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Research Papers

Direct Numerical Control (NC) Path Generation: From Discrete Points to Continuous Spline Paths

[+] Author and Article Information
Yu Liu, Songtao Xia

 Huazhong University of Science and Technology, Wuhan, China, 430074. Illinois Institute of Technology, Chicago, IL 60616Mechanical, Materials and Aerospace Engineering Department,  Illinois Institute of Technology, Chicago, IL 60616

Xiaoping Qian1

 Huazhong University of Science and Technology, Wuhan, China, 430074. Illinois Institute of Technology, Chicago, IL 60616qian@iit.eduMechanical, Materials and Aerospace Engineering Department,  Illinois Institute of Technology, Chicago, IL 60616qian@iit.edu

1

Corresponding author.

J. Comput. Inf. Sci. Eng 12(3), 031002 (Jul 19, 2012) (12 pages) doi:10.1115/1.4006463 History: Received May 15, 2011; Accepted February 07, 2012; Published July 19, 2012; Online July 19, 2012

Spline paths in NC machining are advantageous over linear and circular paths due to their smoothness and compact representation, thus are highly desirable in high-speed machining (HSM) where frequent change of tool position and orientation may lead to inefficient machining, tool wear, and chatter. This paper presents an approach for calculating spline NC paths directly from discrete points with controlled accuracy. Part geometry is represented by discrete points via an implicit point set surface (PSS). Cutter location (CL) points are generated directly from implicit part surfaces and interpolated by B-spline curves. A computing procedure for calculating maximum scallop height is given. The procedure is general and suitable for part surfaces in various surface representations provided that the closest distance from a point to the part surface can be calculated. Our results affirm that the proposed approach can produce high-quality B-spline NC paths directly from discrete points. The resulting spline paths make it possible for directly importing discrete points into Computer Numerical Control (CNC) machines for high-speed machining.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

CC points and CL points defined by Eq. 4 along a path of a wavy surface

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Figure 2

A point on a CL path

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Figure 3

A and B are two points on two consecutive CL paths. The intersection curve of two pipe surfaces PA (t, α) and PB (σ, β) is a scallop curve. C(t, α) is a point on the scallop curve. The scallop height at C(t, α) is h.

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Figure 4

Two sets of synthetic data: (a) a sinusoidal surface and (b) a wavy surface

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Figure 5

Two sets of real scan data: (a) a compound surface and (b) a face-like surface

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Figure 6

CL paths and CL points generated from a sinusoidal surface: (a) isometric view of input points and CL paths; (b) the CL path, interpolated CL points, and corresponding CC points; (c) normal curvatures along the forward direction; and (d) top view of CL points and CL paths

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Figure 7

CL paths and CL points generated from a wavy surface: (a) isometric view of input points and CL paths; (b) the CL path, interpolated CL points, and corresponding CC points; (c) normal curvatures along the forward direction; (d) top view of CL points and CL paths; (e) normal curvatures along the side direction; and (f) top view of CL paths

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Figure 8

CL paths and CL points generated from a compound surface: (a) isometric view of input points and CL paths; (b) the CL path, interpolated CL points, and corresponding CC points; (c) normal curvatures along the forward direction; (d) top view of CL points and CL paths; (e) normal curvatures along the side direction; and (f) top view of CL paths

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Figure 9

CL paths and CL points generated from a face-like surface: (a) isometric view of input points and CL paths; (b) the CL path, interpolated CL points, and corresponding CC points; (c) normal curvatures along the forward direction; (d) top view of CL points and CL paths; (e) normal curvatures along the side direction; and (f) top view of CL paths

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Figure 10

Maximum deviations in the resulting CL paths with respect to the nominal paths by two different approaches: in (a), (c), (e), and (g) where the tolerance requirement is only enforced in the parametric midspan points while in (b), (d), (f), and (h) the tolerance is enforced in the entire curve segments

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Figure 11

Under the same interpolation tolerance, the number of interpolation points in B-spline CL paths is far below the number of interpolation points in linear CL paths: (a) the sinusoidal surface; (b) the wavy surface; (c) the compound surface; and (d) the face-like surface

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