Abstract

This paper presents an easy-to-control volume peeling method for multi-axis machining based on the computation taken on vector fields. The current scalar field-based methods are not flexible and the vector field-based methods do not guarantee the satisfaction of the constraints in the final results. We first conduct an optimization formulation to compute an initial vector field that is well aligned with those anchor vectors specified by users according to different manufacturing requirements. The vector field is further optimized to be an irrotational field so that it can be completely realized by a scalar field’s gradients. Iso-surfaces of the scalar field will be employed as the layers of working surfaces for multi-axis volume peeling in the rough machining. Algorithms are also developed to remove and process singularities of the fields. Our method has been tested on a variety of models and verified by physical experimental machining.

References

1.
Ren
,
L.
,
Sparks
,
T.
,
Ruan
,
J.
, and
Liou
,
F.
,
2010
, “
Integrated Process Planning for a Multiaxis Hybrid Manufacturing System
,”
ASME J. Manuf. Sci. Eng.
,
132
(
2
), p.
021006
.
2.
Lauwers
,
B.
, and
Lefebvre
,
P.
,
2006
, “
Five-Axis Rough Milling Strategies for Complex Shaped Cavities Based on Morphing Technology
,”
CIRP Ann.
,
55
(
1
), pp.
59
62
.
3.
Li
,
Y.
,
Tang
,
K.
, and
Zeng
,
L.
,
2020
, “
A Voxel Model-Based Process-Planning Method for Five-Axis Machining of Complicated Parts
,”
ASME J. Comput. Inf. Sci. Eng.
,
20
(
4
), p.
041012
.
4.
He
,
D.
,
Li
,
Y.
,
Li
,
Z.
, and
Tang
,
K.
,
2021
, “
Geodesic Distance Field-Based Process Planning for Five-Axis Machining of Complicated Parts
,”
ASME J. Manuf. Sci. Eng.
,
143
(
6
), p.
061009
.
5.
Huang
,
B.
,
2013
, “
A Unified Approach for Integrated Computer-Aided Design and Manufacturing
,” Ph.D. thesis,
UCLA
,
Los Angeles, CA
.
6.
Chen
,
L.
,
Li
,
Y.
, and
Tang
,
K.
,
2018
, “
Variable-Depth Multi-Pass Tool Path Generation on Mesh Surfaces
,”
Int. J. Adv. Manuf. Technol.
,
95
(
5
), pp.
2169
2183
.
7.
Zhu
,
J.
,
Tanaka
,
T.
, and
Saito
,
Y.
,
2007
, “
A Rough Cutting Model Generation Algorithm Based on Multi-Resolution Mesh for Sculptured Surface Machining
,”
J. Adv. Mech. Des. Syst., Manuf.
,
1
(
5
), pp.
628
639
.
8.
Kim
,
T.
, and
Sarma
,
S. E.
,
2002
, “
Toolpath Generation Along Directions of Maximum Kinematic Performance; a First Cut at Machine-Optimal Paths
,”
Comput. Aided Des.
,
34
(
6
), pp.
453
468
.
9.
My
,
C. A.
,
Bohez
,
E. L.
,
Makhanov
,
S. S.
,
Munlin
,
M.
,
Phien
,
H. N.
, and
Tabucanon
,
M. T.
,
2005
, “
On 5-Axis Freeform Surface Machining Optimization: Vector Field Clustering Approach
,”
Int. J. CAD/CAM
,
5
(
1
), pp.
1
10
.
10.
Xu
,
K.
, and
Tang
,
K.
,
2014
, “
Five-Axis Tool Path and Feed Rate Optimization Based on the Cutting Force–Area Quotient Potential Field
,”
Int. J. Adv. Manuf. Technol.
,
75
(
9
), pp.
1661
1679
.
11.
Bo
,
P.
, and
Bartoň
,
M.
,
2019
, “
On Initialization of Milling Paths for 5-Axis Flank CNC Machining of Free-Form Surfaces With General Milling Tools
,”
Comput. Aided Geom. Des.
,
71
, pp.
30
42
.
12.
Von Funck
,
W.
,
Theisel
,
H.
, and
Seidel
,
H.-P.
,
2006
, “
Vector Field Based Shape Deformations
,”
ACM Trans. Graphics
,
25
(
3
), pp.
1118
1125
.
13.
Yu
,
Y.
,
Zhou
,
K.
,
Xu
,
D.
,
Shi
,
X.
,
Bao
,
H.
,
Guo
,
B.
, and
Shum
,
H.-Y.
,
2004
, “
“Mesh Editing With Poisson-Based Gradient Field Manipulation
,”
ACM SIGGRAPH 2004 Papers
, August, pp.
644
651
.
14.
Pi
,
J.
,
Red
,
E.
, and
Jensen
,
G.
,
1998
, “
Grind-Free Tool Path Generation for Five-Axis Surface Machining
,”
Comput. Int. Manuf. Syst.
,
11
(
4
), pp.
337
350
.
15.
Li
,
X.
,
1993
, “
Automatic Tool Path Generation for Numerically Controlled Machining of Sculptured Surfaces
,” Doctoral dissertation, University of New Hampshire,
Durham, NC
.
16.
Chien
,
R. T.
, and
Woo
,
T. C.
,
1975
, “
Automatic Program Synthesis: From CAD to CAM
,” Proceedings of the National Computer Conference and Exposition, AFIPS 75,
Association for Computing Machinery
, May 19–22, New York, pp.
813
817
.
17.
Halevi
,
G.
, and
Weill
,
R.
,
1980
, “
Development of Flexible Optimum Process Planning Procedures
,”
CIRP Ann.
,
29
(
1
), pp.
313
317
.
18.
Subrahmanyam
,
S.
, and
Wozny
,
M.
,
1995
, “
An Overview of Automatic Feature Recognition Techniques for Computer-Aided Process Planning
,”
Comput. Ind.
,
26
(
1
), pp.
1
21
.
19.
Liang
,
F.
,
Kang
,
C.
, and
Fang
,
F.
,
2021
, “
A Review on Tool Orientation Planning in Multi-axis Machining
,”
Int. J. Prod. Res.
,
59
(
18
), pp.
5690
5720
.
20.
Kukreja
,
A.
, and
Pande
,
S.
,
2023
, “
An Efficient Iso-Scallop Toolpath Planning Strategy Using Voxel-Based Computer Aided Design Model
,”
ASME J. Comput. Inf. Sci. Eng.
,
23
(
3
), p.
031009
.
21.
Li
,
H.
,
Dong
,
Z.
, and
Vickers
,
G. W.
,
1994
, “
Optimal Toolpath Pattern Identification for Single Island, Sculptured Part Rough Machining Using Fuzzy Pattern Analysis
,”
Comput. Aided Des.
,
26
(
11
), pp.
787
795
.
22.
Heo
,
E.-Y.
,
Kim
,
D.-W.
,
Kim
,
B.-H.
,
Jang
,
D.-K.
, and
Chen
,
F. F.
,
2008
, “
Efficient Roughcut Plan for Machining an Impeller With a 5-Axis NC Machine
,”
Int. J. Comput. Int. Manuf.
,
21
(
8
), pp.
971
983
.
23.
Yuen
,
M.
,
Tan
,
S.
,
Sze
,
W.
, and
Wong
,
W.
,
1987
, “
An Octree Approach to Rough Machining
,”
Proc. Inst. Mech. Eng. Part B: Manage. Eng. Manuf.
,
201
(
3
), pp.
157
163
.
24.
Tseng
,
Y.-J.
,
1999
, “
Machining of Free-Form Solids Using an Octree Volume Decomposition Approach
,”
Int. J. Prod. Res.
,
37
(
1
), pp.
49
72
.
25.
Balasubramaniam
,
M.
,
2001
, “
Automatic 5-Axis NC Toolpath Generation
,” Ph.D. thesis, Massachusetts Institute of Technology,
Cambridge, MA
.
26.
Joneja
,
A.
,
Weifeng
,
Y.
, and
Lee
,
Y.-S.
,
2003
, “
Greedy Tool Heuristic Approach to Rough Milling of Complex Shaped Pockets
,”
IIE Trans.
,
35
(
10
), pp.
953
963
.
27.
Young
,
H.-T.
,
Chuang
,
L.-C.
,
Gerschwiler
,
K.
, and
Kamps
,
S.
,
2004
, “
A Five-Axis Rough Machining Approach for a Centrifugal Impeller
,”
Int. J. Adv. Manuf. Technol.
,
23
(
3
), pp.
233
239
.
28.
Chiou
,
C.-J.
, and
Lee
,
Y.-S.
,
2002
, “
A Machining Potential Field Approach to Tool Path Generation for Multi-Axis Sculptured Surface Machining
,”
Comput. Aided Des.
,
34
(
5
), pp.
357
371
.
29.
Sun
,
S.
,
Sun
,
Y.
,
Xu
,
J.
, and
Lee
,
Y.-S.
,
2018
, “
Iso-Planar Feed Vector-Fields-Based Streamline Tool Path Generation for Five-Axis Compound Surface Machining With Torus-End Cutters
,”
ASME J. Manuf. Sci. Eng.
,
140
(
7
), p.
071013
.
30.
Li
,
Z.
, and
Tang
,
K.
,
2021
, “
Partition-Based Five-Axis Tool Path Generation for Freeform Surface Machining Using a Non-spherical Tool
,”
J. Manuf. Syst.
,
58
(
Part A
), pp.
248
262
.
31.
Fang
,
G.
,
Zhang
,
T.
,
Zhong
,
S.
,
Chen
,
X.
,
Zhong
,
Z.
, and
Wang
,
C. C.
,
2020
, “
Reinforced FDM: Multi-axis Filament Alignment With Controlled Anisotropic Strength
,”
ACM Trans. Graphics
,
39
(
6
), pp.
1
15
.
32.
Li
,
Y.
,
He
,
D.
,
Yuan
,
S.
,
Tang
,
K.
, and
Zhu
,
J.
,
2022
, “
Vector Field-Based Curved Layer Slicing and Path Planning for Multi-Axis Printing
,”
Robot. Comput. Integr. Manuf.
,
77
, p.
102362
.
33.
Mahdavi-Amiri
,
A.
,
Yu
,
F.
,
Zhao
,
H.
,
Schulz
,
A.
, and
Zhang
,
H.
,
2020
, “
VDAC: Volume Decompose-and-Carve for Subtractive Manufacturing
,”
ACM Trans. Graphics
,
39
(
6
), pp.
1
15
.
34.
Liao
,
S.-h.
,
Tong
,
R.-f.
,
Dong
,
J.-x.
, and
Zhu
,
F.-d.
,
2009
, “
Gradient Field Based Inhomogeneous Volumetric Mesh Deformation for Maxillofacial Surgery Simulation
,”
Comput. Graphics
,
33
(
3
), pp.
424
432
.
35.
Kazhdan
,
M.
,
Bolitho
,
M.
, and
Hoppe
,
H.
,
2006
, “
Poisson Surface Reconstruction
,”
Proceedings of the Fourth Eurographics Symposium on Geometry Processing
,
Cagliari Sardinia, Italy
,
June 26–28
, Vol. 7, pp.
61
70
.
36.
Zhang
,
T.
,
Fang
,
G.
,
Huang
,
Y.
,
Dutta
,
N.
,
Lefebvre
,
S.
,
Kilic
,
Z. M.
, and
Wang
,
C. C.
,
2022
, “
S3-Slicer: A General Slicing Framework for Multi-Axis 3d Printing
,”
ACM Trans. Graphics
,
41
(
6
), pp.
1
15
.
37.
Bhatia
,
H.
,
Norgard
,
G.
,
Pascucci
,
V.
, and
Bremer
,
P.-T.
,
2013
, “
The Helmholtz–Hodge Decomposition—A Survey
,”
IEEE Trans. Visualiz. Comput. Graphics
,
19
(
8
), pp.
1386
1404
.
38.
Zhang
,
S.
,
Huang
,
J.
, and
Metaxas
,
D. N.
,
2011
, “
Robust Mesh Editing Using Laplacian Coordinates
,”
Graph. Models
,
73
(
1
), pp.
10
19
.
39.
Crane
,
K.
,
Weischedel
,
C.
, and
Wardetzky
,
M.
,
2013
, “
Geodesics in Heat: A New Approach to Computing Distance Based on Heat Flow
,”
ACM Trans. Graphics
,
32
(
5
), pp.
1
11
.
40.
Spitz
,
S. N.
, and
Requicha
,
A. A.
,
2000
, “
Accessibility Analysis Using Computer Graphics Hardware
,”
IEEE Trans. Visualiz. Comput. Graphics
,
6
(
3
), pp.
208
219
.
41.
Chen
,
N.
, and
Frank
,
M. C.
,
2021
, “
Design for Manufacturing: Geometric Manufacturability Evaluation for Five-Axis Milling
,”
ASME J. Manuf. Sci. Eng.
,
143
(
8
), p.
081007
.
42.
Guennebaud
,
G.
,
Jacob
,
B.
, et al.,
2021
, “Eigen,” No. 3, http://eigen.tuxfamily.org
43.
Wang
,
E.
,
Zhang
,
Q.
,
Shen
,
B.
,
Zhang
,
G.
,
Lu
,
X.
,
Wu
,
Q.
, and
Wang
,
Y.
,
2014
, “Intel Math Kernel Library,”
High-Performance Computing on the Intel® Xeon Phi™: How to Fully Exploit MIC Architectures
,
Springer Cham, Switzerland
, pp.
167
188
.
44.
Gottschalk
,
S.
,
Lin
,
M. C.
, and
Manocha
,
D.
,
1996
, “
Obbtree: A Hierarchical Structure for Rapid Interference Detection
,” Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, pp.
171
180
.
45.
Alexa
,
M.
,
Herholz
,
P.
,
Kohlbrenner
,
M.
, and
Sorkine-Hornung
,
O.
,
2020
, “
Properties of Laplace Operators for Tetrahedral Meshes
,” Computer Graphics Forum, Vol. 39,
Wiley Online Library
, pp.
55
68
.
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