The paper presents a simulation of the Airbus A350-900 wing-to-fuselage assembly process. The latter is a complex multistage process where the compliant parts are being joined by riveting. The current research analyzes the quality of the temporary fastener arrangement. The fastener arrangement is being checked to ensure that the residual gap between joined parts is small, and the fastener loads closing the gap are calculated. The deviations of the part shape from nominal are modeled via initial gaps. A cloud of initial gaps is generated based on the statistical analysis of the available measurements assuming the stochastic nature of local gap roughness. Through the reduction of the corresponding contact problem to a quadratic programming (QP) problem and the use of efficient QP algorithms together with the task-level parallelism, the mass contact problem solving on refined grids is accomplished.

References

References
1.
Chouvion
,
B.
,
Popov
,
A.
,
Ratchev
,
S.
,
Mason
,
C.
, and
Summers
,
M.
,
2011
, “
Interface Management in Wing-Box Assembly
,”
SAE Technical Paper
.
2.
Aderiani
,
A.
,
Wärmefjord
,
K.
, and
Söderberg
,
R.
,
2018
, “
A Multistage Approach to the Selective Assembly of Components Without Dimensional Distribution Assumptions
,”
ASME. J. Manuf. Sci. Eng.
,
140
(
7
), p.
071015
.
3.
Yastrebov
,
V.
,
Anciaux
,
G.
, and
Molinari
,
J.
,
2015
, “
From Infinitesimal to Full Contact Between Rough Surfaces: Evolution of the Contact Area
,”
Int. J. Solids Struct.
52
, pp.
83
102
.
4.
Wang
,
H.
, and
Ding
,
X.
,
2013
, “
Identifying Sources of Variation in Horizontal Stabilizer Assembly Using Finite Element Analysis and Principal Component Analysis
,”
Assem. Automation
,
13
(
1
), pp.
86
96
.
5.
Wärmefjord
,
K.
,
Söderberg
,
R.
,
Lindau
,
B.
,
Lindkvist
,
L.
, and
Lorin
,
S.
,
2016
, “
Joining in Nonrigid Variation Simulation
,”
Computer-aided Technologies
,
R.
Udroiu
, ed.,
IntechOpen
,
London
.
6.
Falgarone
,
H.
,
Thiébaut
,
F.
,
Coloos
,
J.
, and
Mathieu
,
L.
,
2016
, “
Variation Simulation During Assembly of Non-Rigid Components. Realistic Assembly Simulation With Anatoleflex Software
,”
Procedia CIRP
,
43
, pp.
202
207
.
7.
Wang
,
H.
,
Zhang
,
S.
, and
Yu
,
J.
,
2018
, “
Computer Aided Tolerancing of Composite Elevator Assembly Involving Clamping Forces Coordination
,”
Proc. CIRP
,
75
, pp.
256
260
.
8.
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
.
9.
Wärmefjord
,
K.
,
Lindkvist
,
L.
, and
Söderberg
,
R.
,
2008
, “
Tolerance Simulation of Compliant Sheet Metal Assemblies Using Automatic Node-Based Contact Detection
,”
ASME 2008 International Mechanical Engineering Congress and Exposition
,
Boston, MA
, Vol.
14
, pp.
35
44
.
10.
Jareteg
,
C.
,
Wärmefjord
,
K.
,
Cromvik
,
C.
,
Söderberg
,
R.
,
Lindkvist
,
L.
,
Carlson
,
J.
,
Larsson
,
S.
, and
Edelvik
,
F.
,
2014
, “
Geometry Assurance Integrating Process Variation With Simulation of Spring-in for Composite Parts and Assemblies
,”
ASME 2014 International Mechanical Engineering Congress and Exposition
,
Montreal, Quebec, Canada
.
11.
Corrado
,
A.
, and
Polini
,
W.
,
2018
, “
Variation Analysis of Compliant Parts in Composite Material Joined by Adhesive: A Numerical Tool
,”
ASME. J. Manuf. Sci. Eng.
140
(
9
), p.
094502
.
12.
Lupuleac
,
S.
,
Kovtun
,
M.
,
Rodionova
,
O.
, and
Marguet
,
B.
,
2010
, “
Assembly Simulation of Riveting Process
,”
SAE Int. J. Aerosp.
,
2
, pp.
193
198
.
13.
Lupuleac
,
S.
,
Petukhova
,
M.
,
Shinder
,
Y.
, and
Bretagnol
,
B.
,
2011
, “
Methodology for Solving Contact Problem During Riveting Process
,”
SAE Int. J. Aerosp.
,
4
(
2
), pp.
952
957
.
14.
Petukhova
,
M.
,
Lupuleac
,
S.
,
Shinder
,
Y.
,
Smirnov
,
A.
,
Yakunin
,
S.
, and
Bretagnol
,
B.
,
2014
, “
Numerical Approach for Airframe Assembly Simulation
,”
J. Math. Ind.
4
(
1
).
15.
Lupuleac
,
S.
,
Shinder
,
Y.
,
Petukhova
,
M.
,
Yakunin
,
S.
,
Smirnov
,
A.
, and
Bondarenko
,
D.
,
2013
, “
Development of Numerical Methods for Simulation of Airframe Assembly Process
,”
SAE Int. J. Aerosp.
,
6
(
1
), pp.
101
105
.
16.
Lupuleac
,
S.
,
Petukhova
,
M.
,
Stefanova
,
M.
,
Shinder
,
Y.
,
Victorov
,
E.
,
Smirnov
,
A.
, and
Bonhomme
,
E.
,
2015
, “
Simulation of Riveting Process in Case of Unsupported Part Presence
,”
SAE Technical Paper
.
17.
Lupuleac
,
S.
,
Petukhova
,
M.
,
Shinder
,
Y.
,
Stefanova
,
M.
,
Zaitseva
,
N.
,
Pogarskaia
,
T.
, and
Bonhomme
,
E.
,
2016
, “
Software Complex for Simulation of Riveting Process: Concept and Applications
,”
SAE Technical Paper
.
18.
Stefanova
,
M.
,
Yakunin
,
S.
,
Petukhova
,
M.
,
Lupuleac
,
S.
, and
Kokkolaras
,
M.
,
2017
, “
An Interior-Point Method-Based Solver for Simulation of Aircraft Parts Riveting
,”
Eng. Optim.
,
50
(
5
), pp.
781
796
.
19.
Lupuleac
,
S.
,
Zaitseva
,
N.
,
Petukhova
,
M.
,
Shinder
,
Y.
,
Berezin
,
S.
,
Khashba
,
V.
, and
Bonhomme
,
E.
,
2017
, “
Combination of Experimental and Computational Approaches to A320 Wing Assembly
,”
SAE Technical Paper
.
20.
Lupuleac
,
S.
,
Zaitseva
,
N.
,
Stefanova
,
M.
,
Berezin
,
S.
,
Shinder
,
J.
,
Petukhova
,
M.
, and
Bonhomme
,
E.
,
2018
, “
Simulation and Optimization of Airframe Assembly Process
,”
ASME 2018 International Mechanical Engineering Congress and Exposition
,
Pittsburgh, PA
.
21.
Zaitseva
,
N.
,
Lupuleac
,
S.
,
Petukhova
,
M.
,
Churilova
,
M.
,
Pogarskaia
,
T.
, and
Stefanova
,
M.
,
2018
, “
High Performance Computing for Aircraft Assembly Optimization
,”
2018 Global Smart Industry Conference (GloSIC)
,
Chelyabinsk, Russian Federation
.
22.
Pogarskaia
,
T.
,
Churilova
,
M.
,
Petukhova
,
M.
, and
Petukhov
,
E.
,
2018
, “
Simulation and Optimization of Aircraft Assembly Process Using Supercomputer Technologies
,”
Supercomputing. RuSCDays 2018. Communications in Computer and Information Science
, Vol.
965
,
V.
Voevodin
,
S.
Sobolev
, eds.,
Springer
,
Cham
, pp.
367
378
.
23.
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
), p.
011002
.
24.
Lorin
,
S.
,
Lindau
,
B.
,
Tabar
,
R. S.
,
Lindkvist
,
L.
,
Wärmefjord
,
K.
, and
Söderberg
,
R.
,
2018
, “
Efficient Variation Simulation of Spot-Welded Assemblies
,”
ASME 2018 International Mechanical Engineering Congress and Exposition
,
Pittsburgh, Pennsylvania, USA
.
25.
Lorin
,
S.
,
Lindau
,
B.
,
Lindkvist
,
L.
, and
Söderberg
,
R.
,
2019
, “
Efficient Compliant Variation Simulation of Spot-Welded Assemblies
,”
ASME. J. Comput. Inf. Sci. Eng.
,
19
(
1
), p.
011007
.
26.
Yang
,
D.
,
Qu
,
W.
, and
Ke
,
Y.
,
2016
, “
Evaluation of Residual Clearance After Pre-Joining and Pre-Joining Scheme Optimization in Aircraft Panel Assembly
,”
Assem. Automation
,
36
(
4
), pp.
376
387
.
27.
Cheng
,
H.
,
Li
,
Y.
,
Zhang
,
K.
,
Mu
,
W.
, and
Liu
,
B.
,
2011
, “
Variation Modeling of Aeronautical Thin-Walled Structures With Multi-State Riveting
,”
J. Manuf. Syst.
,
30
(
2
), pp.
101
115
.
28.
Lorin
,
S.
,
Lindau
,
B.
,
Lindkvist
,
L.
, and
Söderberg
,
R.
,
2017
, “
Non-Rigid Variation Simulation Using the Sherman-Morrison-Woodbury Formulas
,”
ASME 2017 International Mechanical Engineering Congress and Exposition
,
Tampa, Florida, USA
.
29.
Guittard
,
D.
,
Eve
,
O.
,
Fort
,
F.
,
Colmagro
,
J.
, and
Loyant
,
F.
,
2012
, “
Connection of a Fuselage to an Aircraft Wing
,” U.S. Patent App. 13/428,291.
30.
Merkley
,
K.
,
1998
, “
Tolerance Analysis of Compliant Assemblies
,” Ph.D. thesis,
Brigham Young University
,
Provo, UT
.
31.
Camelio
,
J. A.
,
Hu
,
S. J.
, and
Marin
,
S. P.
,
2004
, “
Compliant Assembly Variation Analysis Using Component Geometric Covariance
,”
ASME J. Manuf. Sci. Eng.
,
126
(
2
), pp.
355
360
.
32.
Bendat
,
J. S.
, and
Piersol
,
A. G.
,
2011
,
Random Data: Analysis and Measurement Procedures
,
4th ed.
,
Wiley, New York
.
33.
Zhang
,
L.
,
Wang
,
H.
,
Li
,
S.
, and
Lin
,
Z.
,
2017
, “
Variation Propagation Modeling and Pattern Mapping Method for Aircraft Assembly Structure Considering Residual Stress from Manufacturing Process
,”
Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture
,
231
(
3
), pp.
437
453
.
34.
Nayak
,
P. R.
,
1973
, “
Random Process Model of Rough Surfaces in Plastic Contact
,”
Wear
,
26
(
3
), pp.
305
333
.
35.
Husu
,
A. P.
,
Wittenberg
,
Y. R.
, and
Palmov
,
V. A.
,
1975
,
Roughness of Surface (Theoretical Probabilistic Approach)
,
Nauka
,
Moscow (in Russian)
.
36.
Palagin
,
Y.
,
Fedotov
,
S.
, and
Shalygin
,
A.
,
1990
, “
Parametric Models for Statistical Simulation of Nonhomogeneous Random Vector Fields
,”
Autom. Remote Control
,
51
(
6
), pp.
789
797
.
37.
Goldfarb
,
D.
, and
Idnani
,
A.
,
1983
, “
A Numerically Stable Dual Method for Solving Strictly Quadratic Programs
,”
Math. Programming
,
27
(
1
), pp.
1
33
.
38.
Powell
,
M. J. D.
,
1985
, “
On the Quadratic Programming Algorithm of Goldfarb and Idnani
,”
Mathematical Programming Essays in Honor of George B. Dantzig
, Vol.
25
, pp.
46
61
.
39.
Mehrotra
,
S.
,
1992
, “
On the Implementation of a Primal Dual Interior Point Method
,”
SIAM J. Optim.
,
2
(
4
), pp.
575
601
.
40.
Bertsekas
,
D. P.
,
1982
, “
Projected Newton Methods for Optimization Problems With Simple Constraints
,”
SIAM J. Control Optim.
,
20
(
2
), pp.
221
246
.
41.
Wang
,
H.
, and
Si
,
S.
,
2014
, “
A FEA Simulation Model for Thin-Walled C-Section Composite Beam Assembling With R-Angle Deviation
,”
ASME 2014 International Mechanical Engineering Congress & Exposition
,
Montreal, Quebec, Canada
.
You do not currently have access to this content.