Research Papers

Spiral Tool Path Generation Method on Mesh Surfaces Guided by Radial Curves

[+] Author and Article Information
Jinting Xu

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

Yukun Ji

School of Automotive Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: 1135428665@qq.com

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

1Corresponding author.

Manuscript received January 28, 2018; final manuscript received April 2, 2018; published online May 14, 2018. Assoc. Editor: Sam Anand.

J. Manuf. Sci. Eng 140(7), 071016 (May 14, 2018) (13 pages) Paper No: MANU-18-1059; doi: 10.1115/1.4039918 History: Received January 28, 2018; Revised April 02, 2018

This paper presents a new spiral smoothing method to generate smooth curved tool paths directly on mesh surfaces. Spiral tool paths are preferable for computer numerical control (CNC) milling, especially for high-speed machining. At present, most spiral tool path generation methods aim mainly for pocketing, and a few methods for machining complex surface also suffer from some inherent problems, such as selection of projecting direction, preprocessing of complex offset contours, easily affected by the mesh or mesh deformation. To address the limitations, a new spiral tool path method is proposed, in which the radial curves play a key role as the guiding curves for spiral tool path generation. The radial curve is defined as one on the mesh surface that connects smoothly one point on the mesh surface and its boundary. To reduce the complexity of constructing the radial curves directly on the mesh surface, the mesh surface is first mapped onto a circular region. In this region, the radial lines, starting from the center, are planned and then mapped inversely onto the mesh surface, thereby forming the desired radial curves. By traversing these radial curves using the proposed linear interpolation method, a polyline spiral is generated, and then, the unfavorable overcuts and undercuts are identified and eliminated by supplementing additional spiral points. Spline-based technique of rounding the corners is also discussed to smooth the polyline spiral, thereby obtaining a smooth continuous spiral tool path. This method is able to not only greatly simplify the construction of radial curves and spiral tool path but also to have the ability of processing and smoothing complex surfaces. Experimental results are presented to validate the proposed method.

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Fig. 1

Spiral tool paths generated by projecting Archimedean spiral in ug/nx: (a) when the slope of the surface increases, the path interval increases, especially when the normal of the surface is vertical to the projecting direction, no spiral tool path is generated and (b) when projecting Archimedean spiral onto the surface of nonrevolution, excessive rapid traversals and interruptions of path appear

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Fig. 2

Undesirable slicing contours for constructing the spiral tool paths: (a) no slicing contours are generated where the normal of the surface normal is parallel to the slicing direction and (b) complex or open slicing contours are generated on complex surfaces that are unfavorable for spiral path construction

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Fig. 3

Undesirable numerical mesh when using PDE-based method to generate spiral tool paths. (a) Three vertices of the triangle at sharp corner all lie on the boundary, (b) magnified view of boundary triangle, and (c) iso-curves of PDE. If three vertices of a triangle lie on the boundary, it is impossible to generate iso-curve in this triangle.

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Fig. 4

Spiral tool paths generated by the mapping-based method: (a) mesh mapping deformation makes the spiral path far away from the sharp corner or the tight curvature regions and (b) uneven distribution of spiral path caused by the deformation in machining denture

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Fig. 5

Planning the planar radial lines on the circular region: (a) Radial lines based on the boundary vertices and (b) radial lines defined by specifying the number of the radial curves

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Fig. 6

(a) The radial lines on the circular region and (b) the corresponding radial curves on the mesh surface. For displaying the figure clearly, only 30 radial curves are generated.

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Fig. 7

Scallop height and the path interval between adjacent tool paths on curved surfaces

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Fig. 8

(a) Overcut and (b) undercut in the interpolated polyline spiral

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Fig. 9

Eliminating overcut and undercut by supplementing additional spiral points

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Fig. 10

Smooth B-spline spiral tool path

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Fig. 11

Spiral tool path on the typical surface of revolution: (a) mesh surface and (b) even and smoothed spiral tool path generated by the proposed method

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Fig. 12

Spiral tool path on the face model: (a) mesh surface, (b) even and smooth spiral tool path generated by the proposed method, (c) zigzag tool path generated using UG/CAM, and (d) one-way tool path generated using UG/CAM

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Fig. 13

Spiral tool path on denture model: (a) dentures and the selected denture for the test and (b) even and smooth spiral tool path generated by the proposed method on the selected denture surface

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Fig. 14

Spiral tool path on complex mold: (a) model of mold with a large number of patches, (b) the selected patches to be machined, (c) mesh model in STL format obtained by triangulating the selected patches, and (d) the spiral tool path generated by the proposed method on the mesh model

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Fig. 15

(a) Spiral tool path generated in nx/cam software and (b) spiral tool path generated by the proposed method

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Fig. 16

(a) Bicycle seat machined by commercial nx/cam software, (b) local magnified view, and (c) bicycle seat machined by smooth spiral tool paths generated by the proposed method




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