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A Study on Partitioning Freeform Surface and Tool Selection Method for 3-Axes CNC Machining

Bui Ngoc Tuyen1, Hoang Van Quy2, Duc-Toan Nguyen1,#orcid
Journal of the Korean Society for Precision Engineering 2019;36(9):813-819.
Published online: September 1, 2019

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#E-mail: toan.nguyenduc@hust.edu.vn, TEL: +84-988-693-047
• Received: April 1, 2019   • Revised: May 9, 2019   • Accepted: May 23, 2019

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A Study on Partitioning Freeform Surface and Tool Selection Method for 3-Axes CNC Machining
J. Korean Soc. Precis. Eng.. 2019;36(9):813-819.   Published online September 1, 2019
DOI: https://doi.org/10.7736/KSPE.2019.36.9.813
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A Study on Partitioning Freeform Surface and Tool Selection Method for 3-Axes CNC Machining
J. Korean Soc. Precis. Eng.. 2019;36(9):813-819.   Published online September 1, 2019
DOI: https://doi.org/10.7736/KSPE.2019.36.9.813
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A Study on Partitioning Freeform Surface and Tool Selection Method for 3-Axes CNC Machining
Image Image Image Image Image Image Image Image Image Image Image
Fig. 1 3D points S(x0, y0, z0) mapping to 2D points S(u0, v0)
Fig. 2 Principal curvatures
Fig. 3 Four popular local surface patch: (a) Concave patch, (b) Convex patch, (c) Planar patch, and (d) Saddle patch
Fig. 4 The algorithm on calculating of tool’s radius
Fig. 5 The points of the planar area and two cases of creating boundary
Fig. 6 The direction of connection neighboring points: (a) 4 links of points and (b) 8 links of points
Fig. 7 An algorithm of creating the boundary of the local freeform patch.
Fig. 8 Local patches and boundaries
Fig. 9 Tool path procedures of (a) sample 1with 3 mm tool diameter and (b) sample 2 with two tools (stage 1-8 mm tool diameter for the convex surface; stage 2-3 mm tool diameter for the concave surface and stage 3 - the final simulation result
Fig. 10 Experimental machining process for sample 2 on 3-axes CNC machine (a), Experimental result of sample 2 (b) and roughness curves occurrence after machining (c)
Fig. 11 The tool path generation for sample 3 (a) and corresponding experiment without roughness at the boundary of the concave patch and planar patch (b)

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

A Study on Partitioning Freeform Surface and Tool Selection Method for 3-Axes CNC Machining

Partitioning free form surface based on K and H

No. Gaussian
curvature		 Mean
curvature		 Local patch
1 K<0 H<0 Concave elliptic
2 H=K<0 Concave umbilic
3 H>0 Convex elliptic
4 K=0 H<0 Concave parabolic
5 H=K=0 Parabolical umbilic
6 H>0 Convex parabolic
7 K>0 H<0 Quasi-concave saddle-like
8 H=0 Minimal saddle-like
9 H>0 Quasi-convex saddle-like
10 H=K>0 Convex umbilic

The net of control points of the B-spline

P00(-50,-50,0) P12(-50,-25,0) P13(-50,0,0) P14(-50,25,0) P15(-50,50,0)
P21(-25,-50,0) P22(-25,-25,0) P23(-25,0,0) P24(-25,25,0) P25(-25,50,0)
P31(0,-50,-20) P32(0,-25,-20 P33(0,0,-15) P34(0,25,0) P35(0,50,20)
P41(25,-50,0) P42(25,-25,0) P43(25,0, 0) P44(25,25,0) P45(25,50,0)
P51(50,-50,0) P52(50,-25,0) P53(50,0,10) P54(50,25,0) P55(50,50,0)

Results of simulation

No. Specification Sample 1 Sample 2 Sample 3
1 Machining time 2h06m40s 1h42m32s 1h40m20s
2 Cutting time 2h05m45s 1h41m25s 1h39m15s
3 Tool change time (s) 20s 30s 30s
4 Tool path length (mm) 231410.219 207724.147 203850.330
5 Cutting length (mm) 227870.088 204098.335 200250.225
Roughing’s Time = 1h9m20s
Table 1 Partitioning free form surface based on K and H
Table 2 The net of control points of the B-spline
Table 3 Results of simulation

Table 1

Table 2

Table 3

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