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Articles

Vol. 10 (2023)

A Review on Variation Modeling of Aircraft Assembly

DOI
https://doi.org/10.31875/2409-9694.2023.10.05
Submitted
September 10, 2023
Published
10.09.2023

Abstract

Abstract: Purpose; The purpose of this paper is to provide a state-of-art review on variation modeling and propagation in aircraft assembly based on process-oriented strategy. And the main focus is on classifying and delineating different approaches, methods, and techniques with critical appraisals of their theories, applications, and limitations, based on which future research directions and corresponding methodologies are proposed.

Design/methodology/approach; To facilitate understanding of the background, this paper starts with a brief description of aircraft assembly. Afterwards, this paper presents a comprehensive review of practical solutions in aircraft variation modeling. Their characteristics are summarized, which serves as a basis for the discussion of deviation control strategies. Thereafter, the possible trends are discussed to facilitate assembly quality control in future research.

References

  1. S. Karmakar and J. Maiti, "A review on dimensional tolerance synthesis: paradigm shift from product to process," Assembly Automation, vol. 32, no. 4, p. p.373-388, 2012. https://doi.org/10.1108/01445151211262438
  2. B. Schleich, N. Anwer, L. Mathieu, and S. Wartzack, "Status and Prospects of Skin Model Shapes for Geometric Variations Management," Procedia CIRP, vol. 43, pp. 154-159, 2016. https://doi.org/10.1016/j.procir.2016.02.005
  3. B. Schleich, N. Anwer, L. Mathieu, and S. Wartzack, "Skin model shapes: A new paradigm shift for geometric variations modelling in mechanical engineering," Computer-Aided Design, vol. 50, pp. 1-15, 2014.
  4. https://doi.org/10.1016/j.cad.2014.01.001
  5. B. Schleich and S. Wartzack, "Novel approaches for the assembly simulation of rigid Skin Model Shapes in tolerance analysis," Computer-Aided Design, vol. 101, pp. 1-11, Aug. 2018. https://doi.org/10.1016/j.cad.2018.04.002
  6. X. Sun, J. Bao, J. Li, Y. Zhang, S. Liu, and B. Zhou, "A digital twin-driven approach for the assembly-commissioning of high precision products," Robotics and Computer-Integrated Manufacturing, vol. 61, p. 101839, Feb. 2020. https://doi.org/10.1016/j.rcim.2019.101839
  7. K. Wang, D. Liu, Z. Liu, Q. Wang, and J. Tan, "An assembly precision analysis method based on a general part digital twin model," Robotics and Computer-Integrated Manufacturing, vol. 68, p. 102089, Apr. 2021. https://doi.org/10.1016/j.rcim.2020.102089
  8. K. Wärmefjord, R. Söderberg, B. Lindau, L. Lindkvist, and S. Lorin, "Joining in nonrigid variation simulation," Computer-aided technologies-applications in engineering and medicine, 2016. https://doi.org/10.5772/65851
  9. Y. Guo, H. Dong, G. Wang, and Y. Ke, "Vibration analysis and suppression in robotic boring process," International Journal of Machine Tools & Manufacture, vol. 101, pp. 102-110, 2016. https://doi.org/10.1016/j.ijmachtools.2015.11.011
  10. G. Liu, H. Huan, and Y. Ke, "Study on analysis and prediction of riveting assembly variation of aircraft fuselage panel," International Journal of Advanced Manufacturing Technology, vol. 75, no. 5-8, pp. 991-1003, 2014. https://doi.org/10.1007/s00170-014-6113-z
  11. W. Zhu, B. Mei, G. Yan, and Y. Ke, "Measurement error analysis and accuracy enhancement of 2D vision system for robotic drilling," Robotics and Computer-Integrated Manufacturing, vol. 30, no. 2, pp. 160-171, Apr. 2014. https://doi.org/10.1016/j.rcim.2013.09.014
  12. Franceschini et al., "Uncertainty evaluation of distributed Large-Scale-Metrology systems by a Monte Carlo approach," CIRP Annals - Manufacturing Technology, vol. 65, no. 1, pp. 491-494, 2016. https://doi.org/10.1016/j.cirp.2016.04.017
  13. J. Lin et al., "Design and development of a ceiling-mounted workshop Measurement Positioning System for large-scale metrology," Optics and Lasers in Engineering, vol. 124, p. 105814, Jan. 2020. https://doi.org/10.1016/j.optlaseng.2019.105814
  14. Q. Wang, P. Huang, J. Li, Y. Ke, B. Yang, and P. G. Maropoulos, "Assembly accuracy analysis for small components with a planar surface in large-scale metrology," Measurement Science & Technology, vol. 27, no. 4, p. 045006, 2016. https://doi.org/10.1088/0957-0233/27/4/045006
  15. D. E. Whitney, "The role of key characteristics in the design of mechanical assemblies," Assembly Automation, vol. 26, no. 4, pp. 315-322, 2006. https://doi.org/10.1108/01445150610705236
  16. D. E. Whitney, Mechanical assemblies : their design, manufacture, and role in product development. Oxford University Press, 2004.
  17. Boeing, "Renton rolls out 47th 737 built at new 47-per-month rate," 2017. https://www.boeing.com
  18. A. C. Thornton, "A Mathematical Framework for the Key Characteristic Process," Research in Engineering Design, vol. 11, no. 3, pp. 145-157, 1999. https://doi.org/10.1007/s001630050011
  19. Y. Cao, X. Li, Z. Zhang, and J. Shang, "Dynamic prediction and compensation of aerocraft assembly variation based on state space model," Assembly Automation, vol. 35, no. 2, pp. 183-189, 2015. https://doi.org/10.1108/AA-06-2014-056
  20. F. Yang, S. Jin, and Z. Li, "A modification of DMVs based state space model of variation propagation for multistage machining processes," Assembly Automation, vol. 37, no. 4, pp. 381-390, 2017. https://doi.org/10.1108/AA-06-2016-052
  21. J. Shi, Stream of Variation Modeling and Analysis for Multistage Manufacturing Processes. Boca Raton: CRC Press, 2006. https://doi.org/10.1201/9781420003901
  22. T. Zhang and J. Shi, "Stream of Variation Modeling and Analysis for Compliant Composite Part Assembly- Part II: Multistation Processes," Journal of Manufacturing Science and Engineering, vol. 138, no. 12, pp. 121004-121004-15, 2016. https://doi.org/10.1115/1.4033282
  23. T. Zhang and J. Shi, "Stream of Variation Modeling and Analysis for Compliant Composite Part Assembly-Part I: Single-Station Processes," Journal of Manufacturing Science and Engineering, vol. 138, no. 12, pp. 121003-121003-15, 2016. https://doi.org/10.1115/1.4033231
  24. K. W. Chase, J. Gao, S. P. Magleby, and C. D. %J A. I. I. E. T. Sorensen, "Including Geometric Feature Variations in Tolerance Analysis of Mechanical Assemblies," vol. 28, no. 10, pp. 795-807, 2000. https://doi.org/10.1080/15458830.1996.11770732
  25. A. Corrado and W. Polini, "Manufacturing signature in variational and vector-loop models for tolerance analysis of rigid parts," The International Journal of Advanced Manufacturing Technology, vol. 88, no. 5-8, pp. 2153-2161, 2017. https://doi.org/10.1007/s00170-016-8947-z
  26. J. Gao, K. W. Chase, and S. P, "Generalized 3-D tolerance analysis of mechanical assemblies with small kinematic adjustments," vol. 30, no. 4, pp. 367-377, 1998. https://doi.org/10.1080/07408179808966476
  27. S. C. Liu and S. J. Hu, "Variation Simulation for Deformable Sheet Metal Assemblies Using Finite Element Methods," Journal of Manufacturing Science and Engineering, vol. 119, no. 3, pp. 368-374, 1997. https://doi.org/10.1115/1.2831115
  28. A. McIlhagger, E. Archer, and R. McIlhagger, "Manufacturing processes for composite materials and components for aerospace applications," in Polymer composites in the aerospace industry, Elsevier, 2015, pp. 53-75. https://doi.org/10.1016/B978-0-85709-523-7.00003-7
  29. C. Nicolas, F. Hugo, T. François, B. Pierre, and G.-E. Moufle, "A New Approach for Best Fit Assembly Based on the Behaviour of Components," SAE Technical Paper, 0148-7191, 2006. https://doi.org/10.4271/2006-01-3174
  30. R. Arista and H. Falgarone, "Flexible Best Fit Assembly of Large Aircraft Components. Airbus A350 XWB Case Study," presented at the Ifip International Conference on Product Lifecycle Management, 2017. https://doi.org/10.1007/978-3-319-72905-3_14
  31. J. Ramirez and J. Wollnack, "Flexible Automated Assembly Systems for Large CFRP-structures," Procedia Technology, vol. 15, pp. 447-455, 2014. https://doi.org/10.1016/j.protcy.2014.09.004
  32. C. Dong, C. Zhang, Z. Liang, and B. Wang, "Dimension variation prediction for composites with finite element analysis and regression modeling," Composites Part A: Applied Science and Manufacturing, vol. 35, no. 6, pp. 735-746, Jun. 2004. https://doi.org/10.1016/j.compositesa.2003.12.005
  33. C. Dong, C. Zhang, Z. Liang, and B. Wang, "Assembly dimensional variation modelling and optimization for the resin transfer moulding process," Modelling & Simulation in Materials Science & Engineering, vol. 12, no. 3, p. S221, 2004. https://doi.org/10.1088/0965-0393/12/3/S11
  34. C. Jareteg et al., "Geometry Assurance Integrating Process Variation With Simulation of Spring-In for Composite Parts and Assemblies," Journal of Computing and Information Science in Engineering.
  35. S. Dahlström and L. Lindkvist, "Variation Simulation of Sheet Metal Assemblies Using the Method of Influence Coefficients With Contact Modeling," Journal of Manufacturing Science and Engineering, vol. 129, no. 3, pp. 615-622, 2006. https://doi.org/10.1115/1.2714570
  36. J. Guo, "Integration of geometric variation and part deformation into variation propagation of 3-D assemblies," International Journal of Production Research.
  37. X. Liao and G. G. Wang, "Non-linear dimensional variation analysis for sheet metal assemblies by contact modeling," Finite Elements in Analysis and Design, vol. 44, no. 1-2, pp. 34-44, 2007. https://doi.org/10.1016/j.finel.2007.08.009
  38. B. Lindau, S. Lorin, L. Lindkvist, and R. Söderberg, "Efficient contact modeling in nonrigid variation simulation," Journal of Computing and Information Science in Engineering, vol. 16, no. 1, p. 011002, 2016. https://doi.org/10.1115/1.4032077
  39. Q. Sun, B. Zhao, X. Liu, X. Mu, and Y. Zhang, "Assembling deviation estimation based on the real mating status of assembly," Computer-Aided Design, vol. 115, pp. 244-255, Oct. 2019. https://doi.org/10.1016/j.cad.2019.06.001
  40. G. Ungemach and F. Mantwill, "Efficient Consideration of Contact in Compliant Assembly Variation Analysis," Journal of Manufacturing Science and Engineering, vol. 131, no. 1, p. 011005, Feb. 2009. https://doi.org/10.1115/1.3046133
  41. "Variation Propagation Analysis on Compliant Assemblies Considering Contact Interaction," Journal of Manufacturing Science and Engineering.
  42. K. Wae rmefjord, L. Lindkvist, and R. Soe derberg, "Tolerance simulation of compliant sheet metal assemblies using automatic node-based contact detection," in ASME International Mechanical Engineering Congress and Exposition, 2008, pp. 35-44. https://doi.org/10.1115/IMECE2008-66344
  43. J. Liu, Z. Zhang, X. Ding, and N. Shao, "Integrating form errors and local surface deformations into tolerance analysis based on skin model shapes and a boundary element method," Computer-Aided Design, vol. 104, pp. 45-59, Nov. 2018. https://doi.org/10.1016/j.cad.2018.05.005
  44. Z. Zhang, Y. Xiao, Y. Xie, and Z. Su, "Effects of contact between rough surfaces on the dynamic responses of bolted composite joints: Multiscale modeling and numerical simulation," Composite Structures, vol. 211, pp. 13-23, 2019. https://doi.org/10.1016/j.compstruct.2018.12.019
  45. W. Qu, X. Lu, and D. Yang, "Influence of pre-joining scheme on panel dynamic characteristic," Journal of Zhejiang University(Engineering Science), vol. 51, no. 2, pp. 336-343, 2017.
  46. D. Yang, W. Qu, and Y. Ke, "Evaluation of residual clearance after pre-joining and pre-joining scheme optimization in aircraft panel assembly," Assembly Automation, 2016. https://doi.org/10.1108/AA-12-2015-129
  47. M. Salehi and P. Sideris, "A finite‐strain gradient‐inelastic beam theory and a corresponding force‐based frame element formulation," International Journal for Numerical Methods in Engineering, vol. 116, no. 6, pp. 380-411, 2018. https://doi.org/10.1002/nme.5929
  48. A. Y. Tamijani and R. K. Kapania, "Chebyshev-ritz approach to buckling and vibration of curvilinearly stiffened plate," AIAA journal, vol. 50, no. 5, pp. 1007-1018, 2012. https://doi.org/10.2514/1.J050042
  49. J. Gerstmayr and A. A. Shabana, "Analysis of thin beams and cables using the absolute nodal co-ordinate formulation," Nonlinear Dynamics, vol. 45, no. 1-2, pp. 109-130, 2006. https://doi.org/10.1007/s11071-006-1856-1
  50. Y. Bi, G. Tu, W. Fang, L. Shen, and R. Li, "Correcting method of hole position for flexible track automatic drilling system," Journal of Zhejiang University(Engineering Science), vol. 49, no. 10, pp. 1863-1869, 2015.
  51. W. W. Cai, C.-C. Hsieh, Y. Long, S. P. Marin, and K. P. Oh, "Digital panel assembly methodologies and applications for compliant sheet components," Journal of Manufacturing Science & Engineering, vol. 128, no. 1, p. 10, 2006. https://doi.org/10.1115/1.2112967
  52. A. Corrado and W. Polini, "Assembly design in aeronautic field: from assembly jigs to tolerance analysis," Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, vol. 231, no. 14, pp. 2652-2663, 2017. https://doi.org/10.1177/0954405416635033
  53. X. Hu, X. Chen, G. Parks, and W. Yao, "Review of improved Monte Carlo methods in uncertainty-based design optimization for aerospace vehicles," Progress in Aerospace Sciences, vol. 86, pp. 20-27, 2016. https://doi.org/10.1016/j.paerosci.2016.07.004
  54. G. F. Abdelal, G. Georgiou, J. Cooper, A. Robotham, A. Levers, and P. Lunt, "Numerical and experimental investigation of aircraft panel deformations during riveting process," Journal of Manufacturing Science and Engineering, vol. 137, no. 1, pp. 9-20, 2015. https://doi.org/10.1115/1.4028923
  55. P. Vichare, O. Martin, and J. Jamshidi, "Dimensional management for aerospace assemblies: framework implementation with case-based scenarios for simulation and measurement of in-process assembly variations," The International Journal of Advanced Manufacturing Technology, vol. 70, no. 1-4, pp. 215-225, 2014. https://doi.org/10.1007/s00170-013-5262-9
  56. H. Wang, "Deformation analysis in horizontal stabilizer assembly using FEA modeling and multilevel analysis," Journal of Aerospace Engineering, vol. 28, no. 2, p. 04014060, 2015. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000385
  57. J. A. Camelio, S. J. Hu, and S. P. Marin, "Compliant assembly variation analysis using component geometric covariance," J. Manuf. Sci. Eng., vol. 126, no. 2, pp. 355-360, 2004. https://doi.org/10.1115/1.1644553
  58. Y. Bi, W. Yan, and Y. Ke, "Optimal placement of measurement points on large aircraft fuselage panels in digital assembly," Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, vol. 231, no. 1, pp. 73-84, 2017. https://doi.org/10.1177/0954405414564808
  59. V. Abedini, M. Shakeri, M. H. Siahmargouei, and H. Baseri, "Analysis of the influence of machining fixture layout on the workpiece's dimensional accuracy using genetic algorithm," Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, vol. 228, no. 11, pp. 1409-1418, 2014. https://doi.org/10.1177/0954405413519605
  60. P. Liu, Y. Li, K. Zhang, and H. Cheng, "Based on region division setup planning for sheet metal assembly in aviation industry," Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 2012. https://doi.org/10.1177/0954405412462656
  61. M. Saadat, L. Cretin, R. Sim, and F. Najafi, "Deformation analysis of large aerospace components during assembly," The International Journal of Advanced Manufacturing Technology, vol. 41, no. 1-2, pp. 145-155, 2009. https://doi.org/10.1007/s00170-008-1464-y
  62. J. Lin, S. Jin, C. Zheng, Z. Li, and Y. Liu, "Compliant assembly variation analysis of aeronautical panels using unified substructures with consideration of identical parts," Computer-Aided Design, vol. 57, pp. 29-40, 2014.
  63. https://doi.org/10.1016/j.cad.2014.07.003
  64. K. Xie, "Analysis, prediction and control of variation propagation in non-linear sheet metal assembly processes," Michigan Technological University, 2009.
  65. N. Rodcheuy, Y. Frostig, and G. A. Kardomateas, "Extended high-order theory for curved sandwich panels and comparison with elasticity," Journal of Applied Mechanics, vol. 84, no. 8, 2017. https://doi.org/10.1115/1.4036612
  66. J. Reddy, "Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates," International Journal of Engineering Science, vol. 48, no. 11, pp. 1507-1518, 2010. https://doi.org/10.1016/j.ijengsci.2010.09.020
  67. R. R. Fernandes and A. Y. Tamijani, "Flutter analysis of laminated curvilinear-stiffened plates," AIAA Journal, vol. 55, no. 3, pp. 998-1011, 2017. https://doi.org/10.2514/1.J055021
  68. E. Carrera, G. Giunta, and M. Petrolo, Beam structures: classical and advanced theories. John Wiley & Sons, 2011. https://doi.org/10.1002/9781119978565
  69. C. Liu, Q. Tian, and H. Hu, "New spatial curved beam and cylindrical shell elements of gradient-deficient Absolute Nodal Coordinate Formulation," Nonlinear Dynamics, vol. 70, no. 3, pp. 1903-1918, 2012. https://doi.org/10.1007/s11071-012-0582-0
  70. M. Jafari and M. Mahjoob, "An exact three-dimensional beam element with nonuniform cross section," Journal of applied mechanics, vol. 77, no. 6, 2010. https://doi.org/10.1115/1.4002000
  71. B. Biondi and S. Caddemi, "Closed form solutions of Euler-Bernoulli beams with singularities," International Journal of Solids and Structures, vol. 42, no. 9-10, pp. 3027-3044, 2005. https://doi.org/10.1016/j.ijsolstr.2004.09.048
  72. W. Su and C. E. Cesnik, "Strain-based geometrically nonlinear beam formulation for modeling very flexible aircraft," International Journal of Solids and Structures, vol. 48, no. 16-17, pp. 2349-2360, 2011. https://doi.org/10.1016/j.ijsolstr.2011.04.012
  73. L. Cheng, Q. Wang, J. Li, and Y. Ke, "Variation modeling for fuselage structures in large aircraft digital assembly," Assembly Automation, 2015. https://doi.org/10.1108/AA-07-2014-069
  74. L. Cheng, Q. Wang, J. Li, and Y. Ke, "Propagation analysis of variation for fuselage structures in multi-station aircraft assembly," Assembly Automation, 2018. https://doi.org/10.1108/AA-03-2017-031
  75. P. M. Sobota, W. Dornisch, R. Müller, and S. Klinkel, "Implicit dynamic analysis using an isogeometric Reissner-Mindlin shell formulation," International Journal for Numerical Methods in Engineering, vol. 110, no. 9, pp. 803-825, 2017. https://doi.org/10.1002/nme.5429
  76. S. P. Timoshenko and S. Woinowsky-Krieger, Theory of plates and shells. McGraw-hill, 1959.
  77. F. Alijani, M. M. Aghdam, and M. Abouhamze, "Application of the extended Kantorovich method to the bending of clamped cylindrical panels," European Journal of Mechanics-A/Solids, vol. 27, no. 3, pp. 378-388, 2008. https://doi.org/10.1016/j.euromechsol.2007.05.011
  78. E. Zappino and E. Carrera, "Multidimensional model for the stress analysis of reinforced shell structures," AIAA Journal, vol. 56, no. 4, pp. 1647-1661, 2018. https://doi.org/10.2514/1.J056384
  79. P. B. Silva, J. Mencik, and J. R. de Franca Arruda, "Wave finite element‐based superelements for forced response analysis of coupled systems via dynamic substructuring," International Journal for Numerical Methods in Engineering, vol. 107, no. 6, pp. 453-476, 2016. https://doi.org/10.1002/nme.5176
  80. D. R. Pacheco, F. D. Marques, and A. J. Ferreira, "Finite element analysis of fluttering plates reinforced by flexible beams: An energy-based approach," Journal of Sound and Vibration, vol. 435, pp. 135-148, 2018. https://doi.org/10.1016/j.jsv.2018.07.042
  81. E. Sapountzakis and V. Mokos, "An improved model for the analysis of plates stiffened by parallel beams with deformable connection," Computers & structures, vol. 86, no. 23-24, pp. 2166-2181, 2008. https://doi.org/10.1016/j.compstruc.2008.06.003
  82. W. C. Slemp, R. K. Kapania, and S. B. Mulani, "Integrated Local Petrov-Galerkin Sinc Method for Structural Mechanics Problems," AIAA journal, vol. 48, no. 6, pp. 1141-1155, 2010. https://doi.org/10.2514/1.45892
  83. A. Y. Tamijani and R. K. Kapania, "Buckling and static analysis of curvilinearly stiffened plates using mesh-free method," AIAA journal, vol. 48, no. 12, pp. 2739-2751, 2010. https://doi.org/10.2514/1.43917
  84. N. Ahmad and R. K. Kapania, "Free Vibration Analysis of Integrally Stiffened Plates with Plate-Strip Stiffeners," AIAA Journal, vol. 54, no. 3, pp. 1107-1119, 2016. https://doi.org/10.2514/1.J054372
  85. G. Chen, M. P. Coleman, D. Ma, P. J. Morris, and P. You, "The fundamental solution for shallow circular cylindrical shells Part I: derivations," International journal of engineering science, vol. 38, no. 11, pp. 1235-1257, 2000. https://doi.org/10.1016/S0020-7225(99)00078-6
  86. S. Kapuria and N. Dhanesh, "Three-dimensional extended Kantorovich solution for accurate prediction of interlaminar stresses in composite laminated panels with interfacial imperfections," Journal of Engineering Mechanics, vol. 141, no. 4, p. 04014140, 2015. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000860
  87. Q. Wang, R. Hou, J. Li, Y. Ke, P. G. Maropoulos, and X. Zhang, "Positioning variation modeling for aircraft panels assembly based on elastic deformation theory," Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, vol. 232, no. 14, pp. 2592-2604, 2018. https://doi.org/10.1177/0954405417697349
  88. Q. Wang, R. Hou, J. Li, and Y. Ke, "Analytical and experimental study on deformation of thin-walled panel with non-ideal boundary conditions," International Journal of Mechanical Sciences, vol. 149, pp. 298-310, 2018. https://doi.org/10.1016/j.ijmecsci.2018.10.001
  89. R. Hou, Q. Wang, J. Li, and Y. Ke, "Modified Fourier-Galerkin solution for aerospace skin-stiffener panels subjected to interface force and mixed boundary conditions," Materials, vol. 12, no. 17, p. 2794, 2019. https://doi.org/10.3390/ma12172794
  90. R. P. G. Muller, "An experimental and analytical investigation on the fatigue behaviour of fuselage riveted lap joints: The significance of the rivet squeeze force, and a comparison of 2024-T3 and Glare 3," 1997.
  91. J. De Rijck, J. Homan, J. Schijve, and R. Benedictus, "The driven rivet head dimensions as an indication of the fatigue performance of aircraft lap joints," International Journal of Fatigue, vol. 29, no. 12, pp. 2208-2218, 2007. https://doi.org/10.1016/j.ijfatigue.2006.12.010
  92. A. Atre and W. Johnson, "Analysis of the effects of interference and sealant on riveted lap joints," Journal of Aircraft, vol. 44, no. 2, pp. 353-364, 2007. https://doi.org/10.2514/1.18320
  93. C. Rans, P. V. Straznicky, and R. Alderliesten, "Riveting process induced residual stresses around solid rivets in mechanical joints," Journal of aircraft, vol. 44, no. 1, pp. 323-329, 2007. https://doi.org/10.2514/1.23684
  94. S. H. Cheraghi, "Effect of variations in the riveting process on the quality of riveted joints," The International journal of advanced manufacturing technology, vol. 39, no. 11-12, pp. 1144-1155, 2008. https://doi.org/10.1007/s00170-007-1291-6
  95. F. R. S. da Cunha, J. A. N. Figueira, and M. C. de Barros, "Methodology to capture induced strains on riveting process of aerospace structures," SAE Technical Paper, 0148-7191, 2010. https://doi.org/10.4271/2010-36-0016
  96. H. Cheng, Y. Li, K. Zhang, W. Mu, and B. Liu, "Variation modeling of aeronautical thin-walled structures with multi-state riveting," Journal of Manufacturing Systems, vol. 30, no. 2, pp. 101-115, 2011. https://doi.org/10.1016/j.jmsy.2011.05.004
  97. F. Aman, S. H. Cheraghi, K. K. Krishnan, and H. Lankarani, "Study of the impact of riveting sequence, rivet pitch, and gap between sheets on the quality of riveted lap joints using finite element method," The International Journal of Advanced Manufacturing Technology, vol. 67, no. 1, pp. 545-562, 2013. https://doi.org/10.1007/s00170-012-4504-6
  98. L. Cheng, Q. Wang, J. Li, and Y. Ke, "A posture evaluation method for a large component with thermal deformation and its application in aircraft assembly," Assembly Automation, vol. 34, no. 3, pp. 275-284, 2014. https://doi.org/10.1108/AA-09-2013-081
  99. I. Masters, X. Fan, R. Roy, and D. Williams, "Modelling distortion induced in an assembly by the self piercing rivet process," Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, vol. 226, no. 2, pp. 300-312, 2012. https://doi.org/10.1177/0954405411414105
  100. Z. Chang, Z. Wang, B. Jiang, J. Zhang, F. Guo, and Y. Kang, "Modeling and predicting of aeronautical thin-walled sheet metal parts riveting deformation," Assembly Automation, 2016. https://doi.org/10.1108/AA-10-2015-077
  101. B. Zheng, H. Yu, and X. Lai, "Assembly deformation prediction of riveted panels by using equivalent mechanical model of riveting process," The International Journal of Advanced Manufacturing Technology, vol. 92, no. 5, pp. 1955-1966, 2017. https://doi.org/10.1007/s00170-017-0262-9
  102. Z. Chang, Z. Wang, L. Xie, Y. Kang, M. Xu, and Z. Wang, "Prediction of riveting deformation for thin-walled structures using local-global finite element approach," Int J Adv Manuf Technol, vol. 97, no. 5-8, pp. 2529-2544, Jul. 2018. https://doi.org/10.1007/s00170-018-2050-6
  103. K. S. Arun, T. S. Huang, and S. D. Blostein, "Least-squares fitting of two 3-D point sets," IEEE Transactions on pattern analysis and machine intelligence, no. 5, pp. 698-700, 1987. https://doi.org/10.1109/TPAMI.1987.4767965
  104. B. K. P. Horn, "Closed-form solution of absolute orientation using unit quaternions," Journal of the Optical Society of America A, vol. 4, no. 4, pp. 629-642, 1987. https://doi.org/10.1364/JOSAA.4.000629
  105. M. W. Walker, L. Shao, and R. A. Volz, "Estimating 3-D location parameters using dual number quaternions," Cvgip Image Understanding, vol. 54, no. 3, pp. 358-367, 1991. https://doi.org/10.1016/1049-9660(91)90036-O
  106. B. K. P. Horn, "Closed-form solution of absolute orientation using orthonormal matrices," Journal of the Optical Society of America A, vol. 5, no. 7, pp. 1127-1135, 1987. https://doi.org/10.1364/JOSAA.5.001127
  107. D. W. Eggert, A. Lorusso, and R. B. Fisher, "Estimating 3-D rigid body transformations: a comparison of four major algorithms," Machine vision and applications, vol. 9, no. 5-6, pp. 272-290, 1997. https://doi.org/10.1007/s001380050048
  108. C. Yu, "3D Points Registration Algorithm with Engineering Constraints," Journal of Mechanical Engineering, vol. 46, no. 05, p. 183, 2010. https://doi.org/10.3901/JME.2010.05.183
  109. L. I. Yuan, L. Zhang, and Y. Wang, "An optimal method of posture adjustment in aircraft fuselage joining assembly with engineering constraints," Chinese Journal of Aeronautics, vol. 30, no. 6, 2017. https://doi.org/10.1016/j.cja.2017.05.006
  110. H. Wang, "Riveting sequence study of horizontal stabilizer assembly using finite-element analysis and riveting equivalent unit," Journal of Aerospace Engineering, vol. 27, no. 6, p. 04014040, 2014. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000368
  111. C. Yu et al., "Compensation method for registration error of laser traker based on three-dimensional anisotropic thermal-deformation theory," Journal of Zhejiang University (Engineering Science), vol. 49, no. 7, pp. 1208-1214, 2015.
  112. L. Wang, C. Z. Sun, J. B. Tan, B. Zhao, and G. Wan, "Improvement of location and orientation tolerances propagation control in cylindrical components assembly using stack-build assembly technique," Assem. Autom., vol. 35, no. 4, pp. 358-366, 2015. https://doi.org/10.1108/AA-03-2015-023
  113. Q. Wang, Y. Dou, J. Li, Y. Ke, P. Keogh, and P. G. Maropoulos, "An assembly gap control method based on posture alignment of wing panels in aircraft assembly," AA, vol. 37, no. 4, pp. 422-433, Sep. 2017, doi: 10.1108/AA-04-2016-031. https://doi.org/10.1108/AA-04-2016-031
  114. B. Rooks, "Automatic wing box assembly developments," Industrial Robot, vol. 28, no. 4, pp. 297-302, 2001. https://doi.org/10.1108/01439910110397101
  115. Y. Bi, W. Yan, and Y. Ke, "Numerical study on predicting and correcting assembly deformation of a large fuselage panel during digital assembly," Assembly Automation, vol. 34, no. 2, pp. 204-216, 2014. https://doi.org/10.1108/AA-04-2013-037
  116. J. Smith, "Concept Development of an Automated Shim Cell for F-35 Forward Fuselage Outer Mold Line Control".
  117. Q. Wang, Y. Dou, J. Li, Y. Ke, P. Keogh, and P. G. Maropoulos, "An assembly gap control method based on posture alignment of wing panels in aircraft assembly," Assembly Automation, vol. 37, no. 4, pp. 422-433, 2017. https://doi.org/10.1108/AA-04-2016-031
  118. Q. Wang, Y. Dou, L. Cheng, and Y. Ke, "Shimming design and optimal selection for non-uniform gaps in wing assembly," Assembly Automation, vol. 37, no. 4, pp. 471-482, 2017. https://doi.org/10.1108/AA-02-2017-021
  119. E. J. K. Voortman Landström, "Influence of liquid shim on the bearing strength of a composite bolted joint." 2019.
  120. N. Zaitseva, S. Lupuleac, M. Petukhova, M. Churilova, T. Pogarskaia, and M. Stefanova, "High Performance Computing for Aircraft Assembly Optimization," presented at the 2018 Global Smart Industry Conference (GloSIC), IEEE, 2018, pp. 1-6. https://doi.org/10.1109/GloSIC.2018.8570136
  121. S. Lupuleac et al., "Combination of Experimental and Computational Approaches to A320 Wing Assembly," SAE International, 2017. https://doi.org/10.4271/2017-01-2085
  122. H.-Y. Dong, G.-S. Cao, W.-W. Qu, and Y.-L. Ke, "Processing research of industry robots drilling and countersinking automaticly," Journal of Zhejiang University (Engineering Science), vol. 47, no. 2, pp. 201-208, 2013.
  123. W. Zhu, W. Qu, and L. Ca, "An off-line programming system for robotic drilling in aerospace manufacturing," International Journal of Advanced Manufacturing Technology, vol. 68, no. 9-12, pp. 2535-2545, 2013. https://doi.org/10.1007/s00170-013-4873-5
  124. H. Dong, H. Zhou, and F. Yin, "Analysis and compensation for absolute positioning error of robot in automatic drilling," Acta Aeronaut Astronaut Sin, vol. 36, no. 7, pp. 2475-2484, 2015.
  125. Q. Wang, S. Zheng, J. Li, Y. Ke, and L. A. Chen, "A correction method for hole positions based on hole margin constraints and Shepard interpolation," Acta Aeronautica et Astronautica Sinica, vol. 36, no. 12, pp. 4025-4034, 2015.
  126. H. J. Xue and J. P. Zhang, "Normal measurement and adjustment for skin drilling," Aeronaut Manuf Technol, vol. 23, no. 60-62, p. 66, 2010.
  127. L. Zhang and X. Wang, "A novel algorithm of normal attitude regulation for the designed end-effector of a flexible drilling robot," Journal of Southeast University, vol. 28, no. 1, pp. 29-34, 2012.
  128. J.-H. JU, M.-Y. ZHOU, and X.-G. HAN, "Normal Adjusting Algorithm of a 3-RPS Parallel Mechanism in Airplane Assembly," China Mechanical Engineering, vol. 22, no. 5, p. 557, 2011.
  129. X. Yue and J. Shi, "Surrogate model-based optimal feed-forward control for dimensional-variation reduction in composite parts' assembly processes," Journal of Quality Technology, vol. 50, no. 3, pp. 279-289, Jul. 2018. https://doi.org/10.1080/00224065.2018.1474688
  130. Y. Wen, X. Yue, J. H. Hunt, and J. Shi, "Feasibility analysis of composite fuselage shape control via finite element analysis," Journal of Manufacturing Systems, vol. 46, pp. 272-281, Jan. 2018. https://doi.org/10.1016/j.jmsy.2018.01.008
  131. X. Yue, Y. Wen, J. H. Hunt, and J. Shi, "Surrogate Model-Based Control Considering Uncertainties for Composite Fuselage Assembly," Journal of Manufacturing Science and Engineering, vol. 140, no. 4, p. 041017, Apr. 2018. https://doi.org/10.1115/1.4038510
  132. J. Du, X. Yue, J. H. Hunt, and J. Shi, "Optimal Placement of Actuators Via Sparse Learning for Composite Fuselage Shape Control," Journal of Manufacturing Science and Engineering, vol. 141, no. 10, p. 101004, Oct. 2019. https://doi.org/10.1115/1.4044249
  133. J. Du, S. Cao, J. H. Hunt, X. Huo, and J. Shi, "A New Sparse-Learning Model for Maximum Gap Reduction of Composite Fuselage Assembly," Technometrics, pp. 1-10, Apr. 2022. https://doi.org/10.1080/00401706.2022.2050817
  134. L. Cheng, Q. Wang, and Y. Ke, "Experimental and numerical analyses of the shimming effect on bolted joints with nonuniform gaps," Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, p. 0954406218809139, 2018. https://doi.org/10.1177/0954406218809139
  135. K. Wang, D. Liu, Z. Liu, Q. Wang, and J. Tan, "An assembly precision analysis method based on a general part digital twin model," Robotics and Computer-Integrated Manufacturing, vol. 68, p. 102089, Apr. 2021. https://doi.org/10.1016/j.rcim.2020.102089
  136. K. Manohar, T. Hogan, J. Buttrick, A. G. Banerjee, J. N. Kutz, and S. L. Brunton, "Predicting shim gaps in aircraft assembly with machine learning and sparse sensing," Journal of Manufacturing Systems, vol. 48, pp. 87-95, Jul. 2018. mhttps://doi.org/10.1016/j.jmsy.2018.01.011