Abstract

Ship assembly involves thousands of large dimensional compliant metal plates. These compliant metal plates are fully welded together by seam welding in the assembly process. Different from the automobile and aerospace assembly process, the final variation of ship assembly is significantly influenced by the geometric nonlinearity and welding deformation generated during the seam welding process. This paper develops a nonlinear variation model (NVM) to consider the geometric nonlinearity, welding shrinkage, and angular distortion based on elastic mechanics. Furthermore, the nonlinear variation model is calibrated by the composite Gaussian process (CGP) to compensate for other factors that are not considered in the nonlinear variation model. The proposed model is validated by a case study on the deviation prediction of an assembly of two compliant metal plates and compared with the existing methods. The results show that the proposed model has a significant improvement in prediction accuracy of assembly deviation.

References

1.
Liu
,
C.
,
Liu
,
J.
,
Zhang
,
Y.
,
Jin
,
S.
,
Wang
,
C.
, and
Lai
,
X.
,
2019
, “
Study on the Propagation of Dimensional Deviation in the Hull Block Building Process
,”
J. Ship Prod. Des.
https://doi.org/10.5957/JSPD.11180040
2.
Jiao
,
Z.
, and
Xing
,
Y.
,
2018
, “
Clamping-Sequence Optimisation Based on Heuristic Algorithm for Sheet-Metal Components
,”
Int. J. Prod. Res.
,
56
(
24
), pp.
7190
7200
. 10.1080/00207543.2017.1410245
3.
Wang
,
J.
,
Rashed
,
S.
, and
Murakawa
,
H.
,
2014
, “
Mechanism Investigation of Welding Induced Buckling Using Inherent Deformation Method
,”
Thin-Walled Struct.
,
80
, pp.
103
119
. 10.1016/j.tws.2014.03.003
4.
Wang
,
R.
,
Zhang
,
J.
,
Serizawa
,
H.
, and
Murakawa
,
H.
,
2009
, “
Study of Welding Inherent Deformations in Thin Plates Based on Finite Element Analysis Using Interactive Substructure Method
,”
Mater. Des.
,
30
(
9
), pp.
3474
3481
. 10.1016/j.matdes.2009.03.015
5.
Liu
,
S. C.
, and
Hu
,
S. J.
,
1997
, “
Variation Simulation for Deformable Sheet Metal Assemblies Using Finite Element Methods
,”
ASME J. Manuf. Sci. Eng.
,
119
(
3
), pp.
368
374
. 10.1115/1.2831115
6.
Jin
,
J.
, and
Shi
,
J.
,
1999
, “
State Space Modeling of Sheet Metal Assembly for Dimensional Control
,”
ASME J. Manuf. Sci. Eng.
,
121
(
4
), pp.
756
762
. 10.1115/1.2833137
7.
Liang
,
W.
,
Deng
,
D.
,
Sone
,
S.
, and
Murakawa
,
H.
,
2005
, “
Prediction of Welding Distortion by Elastic Finite Element Analysis Using Inherent Deformation Estimated Through Inverse Analysis
,”
Welding The World
,
49
(
11–12
), pp.
30
39
. 10.1007/BF03266500
8.
Lindgren
,
L.
,
2001
, “
Finite Element Modeling and Simulation of Welding. Part 3: Efficiency and Integration
,”
J. Therm. Stresses
,
24
(
4
), pp.
305
334
. 10.1080/01495730151078117
9.
Murakawa
,
H.
,
Deng
,
D.
,
Rashed
,
S.
, and
Sato
,
S.
,
2009
, “
Prediction of Distortion Produced on Welded Structures During Assembly Using Inherent Deformation and Interface Element
,”
Trans. JWRI
,
38
(
2
), pp.
63
69
.
10.
Murakawa
,
H.
,
Ma
,
N.
, and
Huang
,
H.
,
2015
, “
Iterative Substructure Method Employing Concept of Inherent Strain for Large-Scale Welding Problems
,”
Welding World
,
59
(
1
), pp.
53
63
. 10.1007/s40194-014-0178-z
11.
Huang
,
H.
,
Wang
,
J.
,
Li
,
L.
, and
Ma
,
N.
,
2016
, “
Prediction of Laser Welding Induced Deformation in Thin Sheets by Efficient Numerical Modeling
,”
J. Mater. Process. Technol.
,
227
, pp.
117
128
. 10.1016/j.jmatprotec.2015.08.002
12.
Cai
,
W. W.
,
Hsieh
,
C.-C.
,
Long
,
Y.
,
Marin
,
S. P.
, and
Oh
,
K. P.
,
2006
, “
Digital Panel Assembly Methodologies and Applications for Compliant Sheet Components
,”
ASME J. Manuf. Sci. Eng.
,
128
(
1
), pp.
270
279
. 10.1115/1.2112967
13.
Mazur
,
M.
,
Leary
,
M.
, and
Subic
,
A.
,
2011
, “
Computer Aided Tolerancing (CAT) Platform for the Design of Assemblies Under External and Internal Forces
,”
Computer-Aided Des.
,
43
(
6
), pp.
707
719
. 10.1016/j.cad.2011.02.004
14.
Lee
,
B.
,
Shalaby
,
M. M.
,
Collins
,
R. J.
,
Crisan
,
V.
,
Walls
,
S. A.
,
Robinson
,
D. M.
, and
Saitou
,
K.
, “
Variation Analysis of Three Dimensional Non-Rigid Assemblies
,”
Proceedings of 2007 IEEE International Symposium on Assembly and Manufacturing
,
Ann Arbor, MI
,
July 22–25
,
IEEE
, pp.
13
18
.
15.
Pahkamaa
,
A.
,
Wärmefjord
,
K.
,
Karlsson
,
L.
,
Söderberg
,
R.
, and
Goldak
,
J.
,
2012
, “
Combining Variation Simulation With Welding Simulation for Prediction of Deformation and Variation of a Final Assembly
,”
ASME J. Comput. Inf. Sci. Eng.
,
12
(
2
), p.
021002
. 10.1115/1.4005720
16.
Wang
,
J.
,
Han
,
J.
,
Domblesky
,
J. P.
,
Li
,
Z.
,
Zhao
,
Y.
, and
Sun
,
L.
,
2017
, “
A Plane Stress Model to Predict Angular Distortion in Single Pass Butt Welded Plates With Weld Reinforcement
,”
ASME J. Manuf. Sci. Eng.
,
139
(
5
), p.
051012
. 10.1115/1.4035469
17.
Lorin
,
S. C.
,
Cromvik
,
C.
,
Edelvik
,
F.
,
Lindkvist
,
L.
, and
Söderberg
,
R.
,
2014
, “
Variation Simulation of Welded Assemblies Using a Thermo-Elastic Finite Element Model
,”
ASME J. Comput. Inf. Sci. Eng.
,
14
(
3
), p.
031003
. 10.1115/1.4027346
18.
Yu
,
K.
,
Jin
,
S.
,
Lai
,
X.
, and
Xing
,
Y.
,
2008
, “
Modeling and Analysis of Compliant Sheet Metal Assembly Variation
,”
Assem. Autom.
,
28
(
3
), pp.
225
234
. 10.1108/01445150810889484
19.
Dahlström
,
S.
, and
Lindkvist
,
L.
,
2007
, “
Variation Simulation of Sheet Metal Assemblies Using the Method of Influence Coefficients With Contact Modeling
,”
ASME J. Manuf. Sci. Eng.
,
129
(
3
), pp.
615
622
. 10.1115/1.2714570
20.
Lupuleac
,
S.
,
Kovtun
,
M.
,
Rodionova
,
O.
, and
Marguet
,
B.
,
2009
, “
Assembly Simulation of Riveting Process
,”
SAE Int. J. Aerosp.
,
2
(
1
), pp.
193
198
. 10.4271/2009-01-3215
21.
Camelio
,
J.
,
Hu
,
S. J.
, and
Ceglarek
,
D.
,
2003
, “
Modeling Variation Propagation of Multi-Station Assembly Systems With Compliant Parts
,”
ASME J. Mech. Des.
,
125
(
4
), pp.
673
681
. 10.1115/1.1631574
22.
Yue
,
J.
,
Camelio
,
J. A.
,
Chin
,
M.
, and
Cai
,
W.
,
2007
, “
Product-Oriented Sensitivity Analysis for Multistation Compliant Assemblies
,”
ASME J. Mech. Des.
,
129
(
8
), pp.
844
851
. 10.1115/1.2735341
23.
Zhang
,
T.
, and
Shi
,
J.
,
2016
, “
Stream of Variation Modeling and Analysis for Compliant Composite Part Assembly—Part I: Single-Station Processes
,”
ASME J. Manuf. Sci. Eng.
,
138
(
12
), p.
121003
. 10.1115/1.4033231
24.
Zhang
,
T.
, and
Shi
,
J.
,
2016
, “
Stream of Variation Modeling and Analysis for Compliant Composite Part Assembly—Part II: Multistation Processes
,”
ASME J. Manuf. Sci. Eng.
,
138
(
12
), p.
121004
. 10.1115/1.4033282
25.
Söderberg
,
R.
,
Wärmefjord
,
K.
, and
Lindkvist
,
L.
,
2015
, “
Variation Simulation of Stress During Assembly of Composite Parts
,”
CIRP Ann. Manuf. Technol.
,
64
(
1
), pp.
17
20
. 10.1016/j.cirp.2015.04.048
26.
Xing
,
Y.
,
2017
, “
Fixture Layout Design of Sheet Metal Parts Based on Global Optimization Algorithms
,”
ASME J. Manuf. Sci. Eng.
,
139
(
10
), p.
101004
. 10.1115/1.4037106
27.
Lorin
,
S.
,
Lindkvist
,
L.
, and
Söderberg
,
R.
,
2014
, “
Variation Simulation of Stresses Using the Method of Influence Coefficients
,”
ASME J. Comput. Inf. Sci. Eng.
,
14
(
1
), p.
011001
. 10.1115/1.4025632
28.
Jin
,
S.
,
Yu
,
K.
,
Lai
,
X.
, and
Liu
,
Y.
,
2009
, “
Sensor Placement Strategy for Fixture Variation Diagnosis of Compliant Sheet Metal Assembly Process
,”
Assembly Autom.
,
29
(
4
), pp.
358
363
. 10.1108/01445150910987772
29.
Lupuleac
,
S.
,
Zaitseva
,
N.
,
Stefanova
,
M.
,
Berezin
,
S.
,
Shinder
,
J.
,
Petukhova
,
M.
, and
Bonhomme
,
E.
,
2019
, “
Simulation of the Wing-to-Fuselage Assembly Process
,”
ASME J. Manuf. Sci. Eng.
,
141
(
6
), p.
061009
. 10.1115/1.4043365
30.
Lupuleac
,
S.
,
Zaitseva
,
N.
,
Petukhova
,
M.
,
Shinder
,
J.
,
Berezin
,
S.
,
Khashba
,
V.
, and
Bonhomme
,
E.
,
2017
, “
Combination of Experimental and Computational Approaches to A320 Wing Assembly
,”
No. 0148-7191
,
SAE Technical Paper
.
31.
Petukhova
,
M. V.
,
Lupuleac
,
S. V.
,
Shinder
,
Y. K.
,
Smirnov
,
A. B.
,
Yakunin
,
S. A.
, and
Bretagnol
,
B.
,
2014
, “
Numerical Approach for Airframe Assembly Simulation
,”
J. Math. Ind.
,
4
(
1
), p.
8
. 10.1186/2190-5983-4-8
32.
Choi
,
W.
, and
Chung
,
H.
,
2015
, “
Variation Simulation of Compliant Metal Plate Assemblies Considering Welding Distortion
,”
ASME J. Manuf. Sci. Eng.
,
137
(
3
), p.
031008
. 10.1115/1.4029755
33.
Choi
,
W.
, and
Chung
,
H.
,
2018
, “
Variation Simulation Model for pre-Stress Effect on Welding Distortion in Multi-Stage Assemblies
,”
Thin-Walled Struct.
,
127
, pp.
832
843
. 10.1016/j.tws.2018.03.018
34.
Liu
,
T.
,
Li
,
Z.-M.
,
Jin
,
S.
, and
Chen
,
W.
,
2019
, “
Compliant Assembly Analysis Including Initial Deviations and Geometric Nonlinearity—Part I: Beam Structure
,”
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
,
233
(
12
), pp.
4233
4246
.
35.
Liu
,
T.
,
Li
,
Z.-M.
,
Jin
,
S.
, and
Chen
,
W.
,
2019
, “
Compliant Assembly Analysis Including Initial Deviations and Geometric Nonlinearity, Part II: Plate Structure
,”
Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci.
,
233
(
11
), pp.
3717
3732
. https://doi.org/10.1177/0954406218806930
36.
Liu
,
T.
,
Li
,
Y.
,
Li
,
B.
,
Li
,
Z.
,
Yao
,
L.
, and
Jin
,
S.
, “
Compliant Variation Analysis for High-Speed Train With Consideration of Welding Distortion
,”
Proceedings of ASME 2018 International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineers
,
David L. Lawrence Convention Center, PA
,
Nov. 9–14
,
American Society of Mechanical Engineers
, p.
V002T002A107
.
37.
Stewart
,
M. L.
, and
Chase
,
K. W.
,
2004
, “
Variation Simulation of Fixtured Assembly Processes for Compliant Structures Using Piecewise-Linear Analysis
,”
Proceedings of ASME 2005 International Mechanical Engineering Congress and Exposition
,
Nov. 5–11, 2005
,
Orlando, FL
,
Paper No: IMECE2005-82371
, pp.
591
600
.
38.
Reddy
,
J. N.
,
2006
,
Theory and Analysis of Elastic Plates and Shells
,
CRC Press
,
Boca Raton, FL
.
39.
Sun
,
W.
, and
Yuan
,
Y.-X.
,
2006
,
Optimization Theory and Methods: Nonlinear Programming
,
Springer Science & Business Media
,
Berlin, Germany
.
40.
Ba
,
S.
, and
Joseph
,
V. R.
,
2012
, “
Composite Gaussian Process Models for Emulating Expensive Functions
,”
Annals Appl. Stat.
,
6
(
4
), pp.
1838
1860
. 10.1214/12-AOAS570
41.
Ba
,
S.
, and
Joseph
,
V. R.
,
2018
, “
Composite Gaussian Process Models. R package version 2.1-1
,” https://CRAN.R-project.org/package=CGP, Accessed 1 May 2019.
42.
Sulaiman
,
M. S.
,
Manurung
,
Y. H. P.
,
Graf
,
M.
, and
Bauer
,
A.
,
2018
, “
Analysis of Weld Induced Distortion of Butt Joint Using Simulation and Experimental Study
,”
J. Mech. Eng.
,
5
(
2
), pp.
78
89
.
43.
Goldak
,
J. A.
, and
Akhlaghi
,
M.
,
2006
,
Computational Welding Mechanics
,
Springer Science & Business Media
,
Berlin, Germany
.
44.
Islam
,
M. R.
,
Buijk
,
A.
,
Raisrohani
,
M.
, and
Motoyama
,
K.
,
2015
, “
Process Parameter Optimization of Lap Joint Fillet Weld Based on FEM-RSM-GA Integration Technique
,”
Adv. Eng. Software
,
79
, pp.
127
136
. 10.1016/j.advengsoft.2014.09.007
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