Inverse problem in laser forming involves the heating position planning and the determination of heating parameters. In this study, the heating positions are optimized in laser forming of single curved shapes based on the processing efficiency. The algorithm uses a probability function to initialize the heating position that is considered to be the bending points. The optimization process is to minimize the total processing time through adjusting the heating positions by considering the boundary conditions of the offset distances, the minimum bending angle, and the minimum distance between two adjacent heating positions. The optimized results are compared with those obtained by the distance-based model as well as the experimental data.

References

References
1.
Shen
,
H.
,
Shi
,
Y. J.
, and
Yao
,
Z. Q.
,
2006
, “
Numerical Simulation of the Laser Forming of Plates Using Two Simultaneous Scans
,”
Comput. Mater. Sci.
,
37
(
3
), pp.
239
245
.
2.
Geiger
,
M.
, and
Vollertsen
,
F.
,
1993
, “
The Mechanisms of Laser Forming
,”
CIRP Ann.
,
42
(
1
), pp.
301
304
.
3.
Kyrsanidi
,
A. K.
,
Kermanidis
,
T. B.
, and
Pantelakis
,
S. G.
,
2000
, “
An Analytical Model for the Prediction of Distortions Caused by the Laser Forming Process
,”
J. Mater. Process. Technol.
,
104
(1–2), pp.
94
102
.
4.
Cheng
,
P. J.
, and
Lin
,
S. C.
,
2001
, “
An Analytical Model to Estimate Angle Formed by Laser
,”
J. Mater. Process. Technol.
,
108
(
3
), pp.
314
319
.
5.
Shen
,
H.
,
Yao
,
Z. Q.
,
Shi
,
Y. J.
, and
Hu
,
J.
,
2006
, “
An Analytical Formula for Estimating the Bending Angle by Laser Forming
,”
Proc. Inst. Mech. Eng., Part C
,
220
(
2
), pp.
243
247
.
6.
Hu
,
Z.
,
Kovacevic
,
R.
, and
Labudovic
,
M.
,
2002
, “
Experimental and Numerical Modeling of Buckling Instability of Laser Sheet Forming
,”
Int. J. Mach. Tools Manuf.
,
42
(
13
), pp.
1427
1439
.
7.
Guan
,
Y. J.
,
Sun
,
S.
,
Zhao
,
G. Q.
, and
Luan
,
Y. G.
,
2003
, “
Finite Element Modeling of Laser Bending of Pre-Loaded Sheet Metals
,”
J. Mater. Process. Technol.
,
142
(
2
), pp.
400
407
.
8.
Liu
,
J.
,
Sun
,
S.
, and
Guan
,
Y. J.
,
2009
, “
Numerical Investigation on the Laser Bending of Stainless Steel Foil With Pre-Stresses
,”
J. Mater. Process. Technol.
,
209
(
3
), pp.
1580
1587
.
9.
Kim
,
J.
, and
Na
,
S. J.
,
2003
, “
Development of Irradiation Strategies for Free Curve Laser Forming
,”
Opt. Laser Technol.
,
35
(
8
), pp.
605
611
.
10.
Kim
,
J.
, and
Na
,
S. J.
,
2009
, “
3D Laser-Forming Strategies for Sheet Metal by Geometrical Information
,”
Opt. Laser Technol.
,
41
(
6
), pp.
843
852
.
11.
Seong
,
W. J.
,
Ahn
,
J.
,
Na
,
S. J.
,
Han
,
M. S.
, and
Jeon
,
Y. C.
,
2010
, “
Geometrical Approach for Flame Forming of Single Curved Ship Hull Plate
,”
J. Mater. Process. Technol.
,
210
(
13
), pp.
1811
1820
.
12.
Abed
,
E.
,
Edwardson
,
S. P.
,
Dearden
,
G.
, and
Watkins
,
K. G.
,
2005
, “
Closed Loop 3-Dimensional Laser Forming of Developable Surfaces
,”
International Workshop on Thermal Forming
,
Bremen, Germany
, Apr. 13–14, pp. 1–21.
13.
Yu
,
G. X.
,
Patrikalakis
,
N. M.
, and
Maekawa
,
T.
,
2000
, “
Optimal Development of Doubly Curved Surfaces
,”
Comput. Aided Geom. Des.
,
17
(
6
), pp.
545
577
.
14.
Liu
,
C.
,
Yao
,
Y. L.
, and
Srinivasan
,
V.
,
2004
, “
Optimal Process Planning for Laser Forming of Doubly Curved Shapes
,”
ASME J. Manuf. Sci. Eng.
,
126
(
1
), pp.
1
9
.
15.
Cheng
,
J.
, and
Yao
,
Y. L.
,
2004
, “
Process Design of Laser Forming for Three-Dimensional Thin Plates
,”
ASME J. Manuf. Sci. Eng.
,
126
(
2
), pp.
217
255
.
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