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Research Papers

A Method of Generating Spiral Tool Path for Direct Three-Axis Computer Numerical Control Machining of Measured Cloud of Point

[+] Author and Article Information
Jinting Xu

School of Automotive Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: xujt@dlut.edu.cn

Longkun Xu

School of Automotive Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: xulongkun@mail.dlut.edu.cn

Yuwen Sun

School of Mechanical Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: xiands@dlut.edu.cn

Yuan-Shin Lee

Department of Industrial and Systems Engineering,
North Carolina State University,
Raleigh, NC 27695
e-mail: yslee@ncsu.edu

Jibin Zhao

State key Laboratory of Robotics,
Shenyang Institute of Automation,
Chinese Academy of Sciences,
Shenyang 110017, China
e-mail: jbzhao@sia.cn

1Corresponding author.

Manuscript received January 28, 2019; final manuscript received April 8, 2019; published online June 13, 2019. Assoc. Editor: Charlie C. L. Wang.

J. Comput. Inf. Sci. Eng 19(4), 041015 (Jun 13, 2019) (12 pages) Paper No: JCISE-19-1025; doi: 10.1115/1.4043532 History: Received January 28, 2019; Accepted April 09, 2019

Smooth continuous spiral tool paths are preferable for computer numerical control (CNC) machining due to their good kinematic and dynamic characteristics. This paper presents a new method to generate spiral tool paths for the direct three-axis CNC machining of the measured cloud of point. In the proposed method, inspired by the Archimedean spiral passing through the radial lines in a circle, 3D radial curves on the cloud of point are introduced, and how to construct the radial curves on the complex cloud of point is discussed in detail and then a practical and effective radial curve construction method of integrating boundary extraction, region triangulation, mesh mapping, and point projection is proposed. On the basis of the radial curves, the spiral tool path can be generated nicely by interpolating the radial curves using a spiral curve. Besides, the method of identifying and eliminating the overcuts and undercuts in the spiral tool path resulting from the interpolation error is also presented for good surface quality. Finally, several examples are given to validate the proposed method and to show its potential in practical applications when quality parametric models and mesh models are not available.

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References

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Figures

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Fig. 1

(a) Practically scattered cloud of point of a car measured by the optical measurement device, ATOS and (b) triangular mesh generated automatically by ATOS, and the larger holes are left by the reference points of ATOS and the smaller are generated by the algorithm of ATOS itself

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Fig. 2

Spiral tool paths on a dental crown: (a) cloud of point of the dental crown and the planar spiral to be projected and (b) spiral tool paths generated by projecting the planar spiral along z-axis using the height correction method. At area “A” where the normal of data point is approximately parallel to z-axis, the path intervals are evenly distributed, but at area “B” with high slope of surface, projecting operation results in the drastic changes of the path intervals.

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Fig. 3

Spiral tool paths on the car hood: (a) cloud of point of the car hood and the planar spiral to be projected and (b) spiral tool paths generated by projecting the planar spiral along z-axis using the height correction method. At area “A” and “B,” the hole defects in practically measured cloud of point lead to some path interruptions that should not occur originally.

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Fig. 4

The Archimedean spiral through the radial lines on the plane. This inspires us to first construct radial curves on the cloud of point and then interpolate these radial curves by a spiral curve for spiral tool path generation.

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Fig. 5

Boundary extraction of planar cloud of point: (a) initial starting point and next boundary point determination and (b) subsequent boundary point extraction

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Fig. 6

The planar radial lines constructed by simply connecting the centroid of the projecting region and the boundary points: (a) available radial lines for interpolating a spiral curve and (b) unavailable radial lines

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Fig. 7

Projecting region triangulation: (a) discretizing the projecting region by a sample point set and (b) triangulating the inner sample points and the boundary points using the Delaunay triangulation method

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Fig. 8

Planar radial curves generation: (a) planar radial lines planned on the circular region and (b) the planar radial curves generated in the projecting region

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Fig. 9

Adjusting the resampling points onto the cloud of point: (a) projection at the area with high slope, (b) approximation error of the radial curve segment to the cloud of point, and (c) projecting the resampling points onto the cloud of point

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Fig. 10

Radial curves generated on the cloud of point of the car hood by the proposed radial curve method

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Fig. 11

Scallop height and path interval along the radial curve

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Fig. 12

Schematic diagram of the linear spiral interpolation among the radial curves

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Fig. 13

(a) Undercuts and (b) overcuts appearing possibly in the initial spiral tool path when the distance between the neighboring spiral points becomes large gradually

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Fig. 14

Eliminating the overcuts in the spiral tool path

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Fig. 15

Spiral tool path on the cloud of point of the car hood: (a) the measured cloud of point of the car hood and (b) the spiral tool path generated by the proposed method

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Fig. 16

Spiral tool path on the cloud of point of the dental crown: (a) the cloud of point of the dental crown and (b) the spiral tool path generated by the proposed method

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Fig. 17

Spiral tool path on the cloud of point of Mickey Mouse’s head: (a) the cloud of point of Mickey Mouse’s head for test and (b) the spiral tool path generated by the proposed method

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