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.
Issue Section:
Research Papers
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
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