Abstract

Geometrical variation is one of the sources of quality issues in a product. Spot welding is an operation that impacts the final geometrical variation of a sheet metal assembly considerably. Evaluating the outcome of the assembly, considering the existing geometrical variation between the components, can be achieved using the method of influence coefficients (MICs), based on the finite element method (FEM). The sequence with which the spot welding operation is performed influences the final geometrical deformations of the assembly. Finding the optimal sequence that results in the minimum geometrical deformation is a combinatorial problem that is experimentally and computationally expensive. Traditionally, spot welding sequence optimization strategies have been to simulate the geometrical variation of the spot-welded assembly after the assembly has been positioned in an inspection fixture. In this approach, the calculation of deformation after springback is one of the most time-consuming steps. In this paper, a method is proposed where the springback calculation in the inspection fixture is bypassed during the sequence evaluation. The results show a significant correlation between the proposed method of weld relative displacements evaluation in the assembly fixture and the assembly deformation in the inspection fixture. Evaluating the relative weld displacement makes each assembly simulation less time-consuming, and thereby, sequence optimization time can be reduced by up to 30%, compared to the traditional approach.

References

1.
Martinsen
,
K.
,
Hu
,
S.
, and
Carlson
,
B.
,
2015
, “
Joining of Dissimilar Materials
,”
CIRP. Ann.
,
64
(
2
), pp.
679
699
. 10.1016/j.cirp.2015.05.006
2.
Söderberg
,
R.
,
Lindkvist
,
L.
,
Wärmefjord
,
K.
, and
Carlson
,
J. S.
,
2016
, “
Virtual Geometry Assurance Process and Toolbox
,”
Procedia CIRP 43, 14th CIRP CAT – CIRP Conference on Computer Aided Tolerancing
,
Gothenburg, Sweden
,
May 18–20
, pp.
3
12
. 10.1016/j.procir.2016.02.043
3.
Anwer
,
N.
,
Ballu
,
A.
, and
Mathieu
,
L.
,
2013
, “
The Skin Model, a Comprehensive Geometric Model for Engineering Design
,”
CIRP. Ann.
,
62
(
1
), pp.
143
146
. 10.1016/j.cirp.2013.03.078
4.
Söderberg
,
R.
,
Wärmefjord
,
K.
,
Carlson
,
J. S.
, and
Lindkvist
,
L.
,
2017
, “
Toward a Digital Twin for Real-Time Geometry Assurance in Individualized Production
,”
CIRP. Ann.
,
66
(
1
), pp.
137
140
. 10.1016/j.cirp.2017.04.038
5.
Franciosa
,
P.
,
Sokolov
,
M.
,
Sinha
,
S.
,
Sun
,
T.
, and
Ceglarek
,
D.
,
2020
, “
Deep Learning Enhanced Digital Twin for Closed-Loop In-Process Quality Improvement
,”
CIRP. Ann.
,
69
(
1
), pp.
369
372
. 10.1016/j.cirp.2020.04.110
6.
Schleich
,
B.
,
Anwer
,
N.
,
Mathieu
,
L.
, and
Wartzack
,
S.
,
2017
, “
Shaping the Digital Twin for Design and Production Engineering
,”
CIRP. Ann.
,
66
(
1
), pp.
141
144
. 10.1016/j.cirp.2017.04.040
7.
Tabar
,
R. S.
,
Wärmefjord
,
K.
, and
Söderberg
,
R.
,
2018
, “
Evaluating Evolutionary Algorithms on Spot Welding Sequence Optimization With Respect to Geometrical Variation
,”
Procedia CIRP 75, The 15th CIRP Conference on Computer Aided Tolerancing
,
Milan, Italy
,
June 11–13
, pp.
421
426
. 10.1016/j.procir.2018.04.061
8.
Tabar
,
R. S.
,
Wärmefjord
,
K.
, and
Söderberg
,
R.
,
2019
, “
A Method for Identification and Sequence Optimisation of Geometry Spot Welds in a Digital Twin Context
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
233
(
16
), pp.
5610
5621
. 10.1177/0954406219854466
9.
Tabar
,
R. S.
,
Wärmefjord
,
K.
,
Söderberg
,
R.
, and
Lindkvist
,
L.
,
2019
, “
A Novel Rule-Based Method for Individualized Spot Welding Sequence Optimization With Respect to Geometrical Quality
,”
ASME J. Manuf. Sci. Eng.
,
141
(
11
), p.
111013
. 10.1115/1.4044254
10.
Wärmefjord
,
K.
,
Söderberg
,
R.
, and
Lindkvist
,
L.
,
2010
, “
Strategies for Optimization of Spot Welding Sequence With Respect to Geometrical Variation in Sheet Metal Assemblies
,” Vol.
3
:
Design and Manufacturing, Parts A and B of ASME International Mechanical Engineering Congress and Exposition
,
Vancouver, British Columbia, Canada
,
Nov. 12–18
, ASME, pp.
569
577
.
11.
Wärmefjord
,
K.
,
Söderberg
,
R.
, and
Lindkvist
,
L.
,
2010
, “
Variation Simulation of Spot Welding Sequence for Sheet Metal Assemblies
,”
Proceedings of NordDesign2010 International Conference on Methods and Tools for Product and Production Development
, Vol.
2
, pp.
Gothenburg, Sweden
,
Aug. 25–27
, The Design Society, pp.
519
528
.
12.
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
, pp.
368
374
. 10.1115/1.2831115
13.
Cai
,
W.
,
Hu
,
S. J.
, and
Yuan
,
J. X.
,
1996
, “
Deformable Sheet Metal Fixturing: Principles, Algorithms, and Simulations
,”
ASME J. Manuf. Sci. Eng.
,
118
(
3
), pp.
318
324
. 10.1115/1.2831031
14.
Polini
,
W.
, and
Corrado
,
A.
,
2020
, “
Methods of Influence Coefficients to Evaluate Stress and Deviation Distribution of Flexible Assemblies—A Review
,”
Int. J. Adv. Manuf. Technol.
,
107
(
5-6
), pp.
2901
2915
. 10.1007/s00170-020-05210-3
15.
Dahlström
,
S.
, and
Lindkvist
,
L.
,
2006
, “
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
16.
Xie
,
K.
,
Wells
,
L.
,
Camelio
,
J. A.
, and
Youn
,
B. D.
,
2007
, “
Variation Propagation Analysis on Compliant Assemblies Considering Contact Interaction
,”
ASME J. Manuf. Sci. Eng.
,
129
(
5
), pp.
934
942
. 10.1115/1.2752829
17.
Lindau
,
B.
,
Lorin
,
S.
,
Lindkvist
,
L.
, and
Söderberg
,
R.
,
2016
, “
Efficient Contact Modeling in Nonrigid Variation Simulation
,”
ASME J. Comput. Inf. Sci. Eng.
,
16
(
1
), pp.
11002
11007
. 10.1115/1.4032077
18.
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
19.
Cai
,
W. W.
,
Hsieh
,
C. -C.
,
Long
,
Y.
,
Marin
,
S. P.
, and
Oh
,
K. P.
,
2005
, “
Digital Panel Assembly Methodologies and Applications for Compliant Sheet Components
,”
ASME J. Manuf. Sci. Eng.
,
128
(
1
), pp.
270
279
. 10.1115/1.2112967
20.
Camelio
,
J.
,
Hu
,
S. J.
, and
Ceglarek
,
D.
,
2004
, “
Modeling Variation Propagation of Multi-Station Assembly Systems With Compliant Parts
,”
ASME J. Mech. Des.
,
125
(
4
), pp.
673
681
. 10.1115/1.1631574
21.
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
22.
Liu
,
C.
,
Liu
,
T.
,
Du
,
J.
,
Zhang
,
Y.
,
Lai
,
X.
, and
Shi
,
J.
,
2020
, “
Hybrid Nonlinear Variation Modeling of Compliant Metal Plate Assemblies Considering Welding Shrinkage and Angular Distortion
,”
ASME J. Manuf. Sci. Eng.
,
142
(
4
), p.
041003
. 10.1115/1.4046250
23.
Lupuleac
,
S.
,
Petukhova
,
M.
,
Shinder
,
Y.
, and
Bretagnol
,
B.
,
2011
, “
Methodology for Solving Contact Problem During Riveting Process
,”
SAE Int. J. Aeros.
, 4(2), pp.
952
957
. 10.4271/2011-01-2582
24.
Lorin
,
S.
,
Lindau
,
B.
,
Lindkvist
,
L.
, and
Söderberg
,
R.
,
2018
, “
Efficient Compliant Variation Simulation of Spot-Welded Assemblies
,”
ASME. J. Comput. Inf. Sci. Eng.
,
19
(
1
), p.
011007
. 10.1115/1.4041706
25.
Liao
,
Y. G.
,
2005
, “
Optimal Design of Weld Pattern in Sheet Metal Assembly Based on a Genetic Algorithm
,”
Int. J. Adv. Manuf. Technol.
,
26
(
5
), pp.
512
516
. 10.1007/s00170-003-2003-5
26.
Xie
,
L. S.
, and
Hsieh
,
C.
,
2002
, “
Clamping and Welding Sequence Optimisation for Minimising Cycle Time and Assembly Deformation
,”
Int. J. Mater. Product Tech.
,
17
(
5-6
), pp.
389
399
. 10.1504/IJMPT.2002.005465
27.
Tabar
,
R. S.
,
Wärmefjord
,
K.
, and
Söderberg
,
R.
,
2020
, “
A New Surrogate Model–based Method for Individualized Spot Welding Sequence Optimization with Respect to Geometrical Quality
,”
Int. J. Adv. Manuf. Technol.
,
106
(
5
), pp.
2333
2346
. 10.1007/s00170-019-04706-x
28.
Tabar
,
R. S.
,
Wärmefjord
,
K.
, and
Söderberg
,
Rikard
,
2020
, “
Rapid Sequence Optimization of Spot Welds for Improved Geometrical Quality Using a Novel Stepwise Algorithm
,”
Engineering Optimization
, 10.1080/0305215X.2020.1757090
29.
Lorin
,
S.
,
Lindau
,
B.
,
Tabar
,
R. S.
,
Lindkvist
,
L.
,
Wörmefjord
,
K.
, and
Söderberg
,
R.
,
2018
, “
Efficient Variation Simulation of Spot-Welded Assemblies
,” Vol.
2
:
Advanced Manufacturing of ASME International Mechanical Engineering Congress and Exposition
,
Pittsburgh, PA
,
Nov. 9–15
, p.
V002T02A110
.
30.
Iversen
,
G. R.
, and
Gergen
,
M.
,
2012
,
Statistics: The Conceptual Approach
,
Springer Science & Business Media
, New York.
31.
Tabar
,
R. S.
,
Wärmefjord
,
K.
,
Söderberg
,
R.
, and
Lindkvist
,
L.
,
2020
, “
Critical Joint Identification for Efficient Sequencing
,”
J. Intell. Manuf.
, 10.1007/s10845-020-01660-4
32.
RD&T Technology AB
,
2017
.
RD&T Software Manual
, Mölndal, Sweden, http://www.rdnt.se
You do not currently have access to this content.