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.

References

References
1.
Tikhon
,
M.
,
Ko
,
T.
,
Lee
,
S.
, and
Sool Kim
,
H.
,
2004
, “
NURBS Interpolator for Constant Material Removal Rate in Open NC Machine Tools
,”
Int. J. Mach. Tools Manuf.
,
44
(
2–3
),
pp.
237
245
.10.1016/j.ijmachtools.2003.10.020
2.
Tsai
,
M.
,
Nien
,
H.
, and
Yau
,
H.
,
2008
, “
Development of an Integrated Look-Ahead Dynamics-Based NURBS Interpolator for High Precision Machinery
,”
Comput.-Aided Des.
,
40
(
5
),
pp.
554
566
.10.1016/j.cad.2008.01.015
3.
Lin
,
A.
, and
Liu
,
H.
,
1998
, “
Automatic Generation of NC Cutter Path From Massive Data Points
,”
Comput.-Aided Des.
,
30
(
1
),
pp.
77
90
.10.1016/S0010-4485(97)00066-3
4.
Park
,
S.
, and
Chung
,
Y.
,
2003
, “
Tool-Path Generation From Measured Data
,”
Comput.-Aided Des.
,
35
(
5
),
pp.
467
475
.10.1016/S0010-4485(02)00070-2
5.
Park
,
S.
,
2004
, “
Sculptured Surface Machining Using Triangular Mesh Slicing
,”
Comput.-Aided Des.
,
36
(
3
),
pp.
279
288
.10.1016/S0010-4485(03)00114-3
6.
Feng
,
H.
, and
Teng
,
Z.
,
2005
, “
Iso-Planar Piecewise Linear NC Tool Path Generation From Discrete Measured Data Points
,”
Comput.-Aided Des.
,
37
(
1
),
pp.
55
64
.10.1016/j.cad.2004.04.001
7.
Chui
,
K.
,
Chiu
,
W.
, and
Yu
,
K.
,
2008
, “
Direct 5-Axis Tool-Path Generation From Point Cloud Input Using 3D Biarc Fitting
,”
Rob. Comput.-Integr. Manufact.
,
24
(
2
),
pp.
270
286
.10.1016/j.rcim.2006.11.004
8.
Park
,
S.
, and
Shin
,
H.
,
2009
, “
Machining Tool Path Generation for Point Set
,”
Int. J. CAD/CAM
,
8
(
1
), pp.
45
83
.
9.
Zhang
,
D.
,
Yang
,
P.
, and
Qian
,
X.
,
2009
, “
Adaptive NC Path Generation From Massive Point Data With Bounded Error
,”
ASME J. Manuf. Sci. Eng.
,
131
, p.
011001
.10.1115/1.3010710
10.
Tam
,
H.
,
Xu
,
H.
, and
Zhou
,
Z.
,
2002
, “
Iso-Planar Interpolation for the Machining of Implicit Surfaces
,”
Comput.-Aided Des.
,
34
(
2
),
pp.
125
136
.10.1016/S0010-4485(01)00059-8
11.
Lartigue
,
C.
,
Thiebaut
,
F.
, and
Maekawa
,
T.
,
2001
, “
CNC Tool Path in Terms of B-Spline Curves
,”
Comput.-Aided Des.
,
33
(
4
),
pp.
307
319
.10.1016/S0010-4485(00)00090-7
12.
Jin
,
Y.
,
Wang
,
Y.
,
Feng
,
J.
, and
Yang
,
J.
,
2010
, “
Research on Consecutive Micro-Line Interpolation Algorithm With Local Cubic B-Spline Fitting for High Speed Machining
,”
IEEE Proceedings of International Conference on Mechatronics and Automation (ICMA)
,
pp.
1675
1680
.
13.
Erkorkmaz
,
K.
, and
Altintas
,
Y.
,
2001
, “
High Speed CNC System Design. Part I: Jerk Limited Trajectory Generation and Quintic Spline Interpolation
,”
Int. J. Mach. Tools Manuf.
,
41
(
9
),
pp.
1323
1345
.10.1016/S0890-6955(01)00002-5
14.
Vijayaraghavan
,
A.
,
Sodemann
,
A.
,
Hoover
,
A.
, Rhett
Mayor
,
J.
, and
Dornfeld
,
D.
,
2010
, “
Trajectory Generation in High-Speed, High-Precision Micromilling Using Subdivision Curves
,”
Int. J. Mach. Tools Manuf.
,
50
(
4
),
pp.
394
403
.10.1016/j.ijmachtools.2009.10.010
15.
Amenta
,
N.
, and
Kil
,
Y.
,
2004
, “
Defining Point-Set Surfaces
,”
ACM Trans. Graphics
,
23
(
3
),
pp.
264
270
.10.1145/1015706.1015713
16.
Choi
,
B.
, and
Jerard
,
R.
,
1998
,
Sculptured Surface Machining: Theory and Applications
,
Kluwer Academic
,
Dordrecht
, Netherland.
17.
Lasemi
,
A.
,
Xue.
,
D.
, and
Gu
,
P.
,
2010
, “
Recent Development in CNC Machining of Freeform Surfaces: A State-of-Art Review
,”
Comput.-Aided Des.
,
42
(
7
),
pp.
641
654
.10.1016/j.cad.2010.04.002
18.
Levin
,
D.
,
2003
, “
Mesh-Independent Surface Interpolation
,”
Geom. Model. Sci. Vis.
, Edited by Brunnett, Hamann and Mueller,
Springer-Verlag
, 2003, pp.
37
49
.
19.
Alexa
,
M.
,
Behr
,
J.
,
Cohen-Or
,
D.
,
Fleishman
,
S.
,
Levin
,
D.
, and
Silva
,
C.
,
2003
, “
Computing and Rendering Point Set Surfaces
,”
IEEE Trans. Vis. Comput. Graph.
,
9
(
1
),
pp.
3
15
.10.1109/TVCG.2003.1175093
20.
Yang
,
P.
, and
Qian
,
X.
,
2008
, “
Adaptive Slicing of Moving Least Squares Surfaces: Toward Direct Manufacturing of Point Set Surfaces
,”
ASME J. Comput. Inf. Sci. Eng.
,
8
, p.
031003
.10.1115/1.2955481
21.
Sarma
,
R.
, and
Dutta
,
D.
,
1997
, “
The Geometry and Generation of NC Tool Paths
,”
ASME J. Mech. Des.
,
119
,
pp.
253
258
.10.1115/1.2826244
22.
Yang
,
P.
, and
Qian
,
X.
,
2007
, “
Direct Computing of Surface Curvatures for Point-Set Surfaces
,”
Proceedings of Eurographics Symposium on Point-Based Graphics
,
pp.
29
36
.
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