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Compliant assembly variation modeling for thin-walled structures considering clamping constraints and geometric deviations based on isogeometric analysis

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Abstract

Geometric deviations and assembly deformations are inevitable in compliant assembly processes and have a significant impact on assembly quality. This paper proposes a variation propagation model based on isogeometric analysis (IGA), which unifies geometric deviations and compliant deformations in one framework by embedding exact geometry into assembly analysis. First, geometric deviations are modeled via offsets along control points using non-uniform rational basis spline (NURBS). Then, the elastic force induced by geometric deviation is calculated using Kirchhoff–Love shell elements. Further, clamping constraints, such as fixture positioning deviation and connection matching deviation, are transformed into displacement boundary conditions using the Lagrange multiplier method. Finally, several examples including the practical project cases are provided to demonstrate the accuracy and efficiency of the developed method in obtaining assembly deviation distributions.

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References

  1. Camelio JA, Hu SJ, Marin SP (2004) Compliant assembly variation analysis using component geometric covariance. J Manuf Sci Eng 126:355–360. https://doi.org/10.1115/1.1644553

    Article  Google Scholar 

  2. Franciosa P, Gerbino S, Patalano S (2011) Simulation of variational compliant assemblies with shape errors based on morphing mesh approach. Int J Adv Manuf Technol 53:47–61. https://doi.org/10.1007/s00170-010-2839-4

    Article  Google Scholar 

  3. Sánchez-Reyes J, Chacón JM (2012) Hermite approximation for free-form deformation of curves and surfaces. Comput Aided Des 44:445–456. https://doi.org/10.1016/j.cad.2012.01.001

    Article  Google Scholar 

  4. Zhang Z, Zhang Z, Jin X, Zhang Q (2018) A novel modelling method of geometric errors for precision assembly. Int J Adv Manuf Technol 94:1139–1160. https://doi.org/10.1007/s00170-017-0936-3

    Article  Google Scholar 

  5. Luo C, Franciosa P, Ceglarek D, Ni Z, Jia F (2018) A novel geometric tolerance modeling inspired by parametric space envelope. Ieee T Autom Sci Eng 15:1386–1398. https://doi.org/10.1109/tase.2018.2793920

    Article  Google Scholar 

  6. Babu M, Franciosa P, Shekhar P, Ceglarek D (2023) Object shape error modelling and simulation during early design phase by morphing Gaussian random fields. Comput-Aided Des 158:103481. https://doi.org/10.1016/j.cad.2023.103481

    Article  MathSciNet  Google Scholar 

  7. Dantan JY, Ballu A, Mathieu L (2008) Geometrical product specifications — model for product life cycle. Comput Aided Des 40:493–501. https://doi.org/10.1016/j.cad.2008.01.004

    Article  Google Scholar 

  8. Anwer N, Ballu A, Mathieu L (2013) The skin model, a comprehensive geometric model for engineering design. Cirp Ann - Manuf Technol 62:143–146. https://doi.org/10.1016/j.cirp.2013.03.078

    Article  Google Scholar 

  9. Schleich B, Wartzack S (2015) Approaches for the assembly simulation of skin model shapes. Comput Aided Des 65:18–33. https://doi.org/10.1016/j.cad.2015.03.004

    Article  Google Scholar 

  10. Huang W, Ceglarek D (2002) Mode-based decomposition of part form error by discrete-cosine-transform with implementation to assembly and stamping system with compliant parts. CIRP Ann - Manuf Technol 51:21–26. https://doi.org/10.1016/s0007-8506(07)61457-7

    Article  Google Scholar 

  11. Huang W, Liu J, Chalivendra V, Ceglarek D, Kong Z, Zhou Y (2014) Statistical modal analysis for variation characterization and application in manufacturing quality control. Iie Trans 46:497–511. https://doi.org/10.1080/0740817x.2013.814928

    Article  Google Scholar 

  12. Samper S, Formosa F (2007) Form defects tolerancing by natural modes analysis. J Comput Inf Sci Eng 7:44–51. https://doi.org/10.1115/1.2424247

    Article  Google Scholar 

  13. Grandjean J, Ledoux Y, Samper S (2013) On the role of form defects in assemblies subject to local deformations and mechanical loads. Int J Adv Manuf Technol 65:1769–1778. https://doi.org/10.1007/s00170-012-4298-6

    Article  Google Scholar 

  14. Homri L, Goka E, Levasseur G, Dantan JY (2017) Tolerance analysis — form defects modeling and simulation by modal decomposition and optimization. Comput Aided Des 91:46–59. https://doi.org/10.1016/j.cad.2017.04.007

    Article  Google Scholar 

  15. Li Y, Zhao Y, Yu H, Lai X (2017) Compliant assembly variation analysis of sheet metal with shape errors based on primitive deformation patterns. Proc Inst Mech Eng Part C J Mech Eng Sci 232:2334–2351. https://doi.org/10.1177/0954406217720231

    Article  Google Scholar 

  16. Cao YL, Li B, Ye XF, Guan JY, Yang JX (2015) Geometrical simulation of multiscale toleranced surface with consideration of the tolerancing principle. J Comput Inf Sci Eng 15:021006. https://doi.org/10.1115/1.4028962

    Article  Google Scholar 

  17. Liu SC, Hu SJ (1997) Variation simulation for deformable sheet metal assemblies using finite element methods. J Manuf Sci Eng 119:368–374. https://doi.org/10.1115/1.2831115

    Article  Google Scholar 

  18. Camelio J, Hu SJ, Ceglarek D (2003) Modeling variation propagation of multi-station assembly systems with compliant parts. J Mech Des 125:673–681. https://doi.org/10.1115/1.1631574

    Article  Google Scholar 

  19. Zhang T, Shi J (2016) Stream of variation modeling and analysis for compliant composite part assembly— part II: multistation processes. J Manuf Sci Eng 138:121004. https://doi.org/10.1115/1.4033282

    Article  Google Scholar 

  20. Zhang T, Shi J (2016) Stream of variation modeling and analysis for compliant composite part assembly—part I: single-station processes. J Manuf Sci Eng 138:121003. https://doi.org/10.1115/1.4033231

    Article  Google Scholar 

  21. Choi W, Chung H (2018) Variation simulation model for pre-stress effect on welding distortion in multi-stage assemblies. Thin Wall Struct 127:832–843. https://doi.org/10.1016/j.tws.2018.03.018

    Article  Google Scholar 

  22. Choi W, Chung H (2015) Variation simulation of compliant metal plate assemblies considering welding distortion. J Manuf Sci Eng 137:031008. https://doi.org/10.1115/1.4029755

    Article  Google Scholar 

  23. Atik H, Chahbouni M, Amagouz D, Boutahari S (2018) An analysis of springback of compliant assemblies by contact modeling and welding distortion. Int J Eng Technol 7:85–89. https://doi.org/10.14419/ijet.v7i1.8330

    Article  Google Scholar 

  24. Abdelal GF, Georgiou G, Cooper J, Robotham A, Levers A, Lunt P (2015) Numerical and experimental investigation of aircraft panel deformations during riveting process. J Manuf Sci Eng 137:011009. https://doi.org/10.1115/1.4028923

    Article  Google Scholar 

  25. Liu T, Li Z, Jin S, Chen W (2018) Compliant assembly analysis including initial deviations and geometric nonlinearity, part II: plate structure. Proc Inst Mech Eng Part C J Mech Eng Sci 233:3717–3732. https://doi.org/10.1177/0954406218806930

    Article  Google Scholar 

  26. Liu T, Li Z, Jin S, Chen W (2018) Compliant assembly analysis including initial deviations and geometric nonlinearity—Part I: beam structure. Proc Inst Mech Eng Part C J Mech Eng Sci 233:4233–4246. https://doi.org/10.1177/0954406218813392

    Article  Google Scholar 

  27. Liu C, Liu T, Du J, Zhang Y, Lai X, Shi J (2020) Hybrid nonlinear variation modeling of compliant metal plate assemblies considering welding shrinkage and angular distortion. J Manuf Sci Eng 142:041003. https://doi.org/10.1115/1.4046250

    Article  Google Scholar 

  28. Yu H, Zhao C, Lai X (2018) Compliant assembly variation analysis of scalloped segment plates with a new irregular quadrilateral plate element via ANCF. J Manuf Sci Eng 140:091006. https://doi.org/10.1115/1.4040323

    Article  Google Scholar 

  29. Yu H, Zhao C, Zheng B, Wang H (2018) Compliant assembly variation analysis of thin-walled structures based on the absolute nodal coordinate formulation. Assem Autom 38:125–141. https://doi.org/10.1108/aa-05-2016-046

    Article  Google Scholar 

  30. Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Method Appl M 194:4135–4195. https://doi.org/10.1016/j.cma.2004.10.008

    Article  MathSciNet  Google Scholar 

  31. Huynh GD, Zhuang X, Bui HG, Meschke G, Nguyen-Xuan H (2020) Elasto-plastic large deformation analysis of multi-patch thin shells by isogeometric approach. Finite Elem Anal Des 173:103389. https://doi.org/10.1016/j.finel.2020.103389

    Article  MathSciNet  Google Scholar 

  32. Peng X, Xu G, Zhou A, Yang Y, Ma Z (2020) An adaptive Bernstein-Bézier finite element method for heat transfer analysis in welding. Adv Eng Softw 148:102855. https://doi.org/10.1016/j.advengsoft.2020.102855

    Article  Google Scholar 

  33. Modirkhazeni SM, Bhigamudre VG, Trelles JP (2020) Evaluation of a nonlinear variational multiscale method for fluid transport problems. Comput Fluids 209:104531. https://doi.org/10.1016/j.compfluid.2020.104531

    Article  MathSciNet  Google Scholar 

  34. Hosters N, Helmig J, Stavrev A, Behr M, Elgeti S (2018) Fluid–structure interaction with NURBS-based coupling. Comput Method Appl M 332:520–539. https://doi.org/10.1016/j.cma.2018.01.003

    Article  MathSciNet  Google Scholar 

  35. Rupal BS, Anwer N, Secanell M, Qureshi AJ (2020) Geometric tolerance and manufacturing assemblability estimation of metal additive manufacturing (AM) processes. Mater Des 194:108842. https://doi.org/10.1016/j.matdes.2020.108842

    Article  Google Scholar 

  36. Piegl L, Tiller W (1997) The NURBS Book. Monogr Vis Commun. https://doi.org/10.1007/978-3-642-59223-2

    Article  Google Scholar 

  37. Ludwig T, Hühne C, Lorenzis LD (2019) Rotation-free Bernstein-Bézier elements for thin plates and shells – development and validation. Comput Method Appl M 348:500–534. https://doi.org/10.1016/j.cma.2019.01.039

    Article  Google Scholar 

  38. Zareh M, Qian X (2019) Kirchhoff-Love shell formulation based on triangular isogeometric analysis. Comput Method Appl M 347:853–873. https://doi.org/10.1016/j.cma.2018.12.034

    Article  MathSciNet  Google Scholar 

  39. Chen L, Nguyen-Thanh N, Nguyen-Xuan H, Rabczuk T, Bordas SPA, Limbert G (2014) Explicit finite deformation analysis of isogeometric membranes. Comput Method Appl M 277:104–130. https://doi.org/10.1016/j.cma.2014.04.015

    Article  MathSciNet  Google Scholar 

  40. Hirschler T, Bouclier R, Dureisseix D, Duval A, Elguedj T, Morlier J (2019) A dual domain decomposition algorithm for the analysis of non-conforming isogeometric Kirchhoff-Love shells. Comput Method Appl M 357:112578. https://doi.org/10.1016/j.cma.2019.112578

    Article  MathSciNet  Google Scholar 

  41. Schuß S, Dittmann M, Wohlmuth B, Klinkel S, Hesch C (2019) Multi-patch isogeometric analysis for Kirchhoff-Love shell elements. Comput Method Appl M 349:91–116. https://doi.org/10.1016/j.cma.2019.02.015

    Article  MathSciNet  Google Scholar 

  42. Liu N, Jeffers AE (2018) A geometrically exact isogeometric Kirchhoff plate: feature-preserving automatic meshing and C1 rational triangular Bézier spline discretizations. Int J Numer Meth Eng 115:395–409. https://doi.org/10.1002/nme.5809

    Article  Google Scholar 

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Funding

The work described in this paper is supported in part by grants from the National Natural Science Foundation of China (award numbers: 51775346 and 52005334) and the Natural Science Foundation of Chongqing, China (Grant No. cstc2021jcyj-msxmX1104).

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Authors and Affiliations

  1. State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Jinyu Liu & Yanzheng Zhao

  2. State Key Laboratory of Ocean Engineering, Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Zhimin Li & Tao Liu

Authors
  1. Jinyu Liu
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  2. Zhimin Li
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  3. Tao Liu
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  4. Yanzheng Zhao
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Contributions

Jinyu Liu: conceptualization; methodology; software; validation; visualization; writing—original draft; writing—review and editing.

Zhi-Min Li: conceptualization; methodology; validation; visualization; supervision; writing—review and editing.

Tao Liu: validation; visualization; supervision; writing—review and editing.

Yanzheng Zhao: validation; visualization; supervision; writing—review and editing.

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Correspondence to Zhimin Li.

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Liu, J., Li, Z., Liu, T. et al. Compliant assembly variation modeling for thin-walled structures considering clamping constraints and geometric deviations based on isogeometric analysis. Int J Adv Manuf Technol 132, 127–146 (2024). https://doi.org/10.1007/s00170-024-13248-w

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