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The inspection of deformable bodies using curvature estimation and Thompson-Biweight test

  • Ali AidibeEmail author
  • Antoine Tahan
ORIGINAL ARTICLE

Abstract

Dimensioning and tolerancing standards assume inspection operation, unless otherwise specified, must be done in Free State. This can be problematic when dealing with compliant parts. The inspection of compliant parts needs specialized fixtures because in Free State they may have a significantly different form than their nominal model (CAD) due to inherent variations in the manufacturing process, gravity loads, and residual strains. These specialized fixtures pose difficulties, bear significant costs to industry, and the process is very time-consuming. To address these challenges, this paper proposes a new method for quantifying flexibility/rigidity of the mechanical parts. Subsequently, a novel approach named IDB-CTB is proposed to fixtureless inspection of deformable bodies by curvature estimation and Thompson-Biweight test. This approach combines the Gaussian curvature properties of manufactured compliant parts, one of the intrinsic properties of the geometry, with the Thompson-Biweight statistical test based on the extreme value notion as an identification method. The aim is to distinguish profile deviation due to the manufacturing process from a part’s deformation due to its flexibility in order to determine whether the tolerance fits the CAD model or not. The IDB-CTB approach is tested on two sets of case studies. Three simulated, typical industrial sheet metal case studies were performed in the first set, and an experimental case study in the second one. The low percentage of errors in defect areas and in the profile deviations estimated compared with their reference ones in most cases reflects the effectiveness of the proposed approach.

Keywords

Curvature Registration Inspection Metrology Compliant Non-rigid Deformation GD&T Fixtureless Intrinsic geometry 

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References

  1. 1.
    ASMEY14.5-2009 (2009) Dimensioning and tolerancing. The American Society of Mechanical Engineers National Standard, The American Society of Mechanical Engineers, New YorkGoogle Scholar
  2. 2.
    ISO 10579 (2010) “Geometrical product specifications (GPS)—dimensioning and tolerancing—non rigid parts. International Organization for Standardization (ISO), GenevaGoogle Scholar
  3. 3.
    G. Abenhaim, A. Desrochers, and A. Tahan (2012) “Nonrigid parts’ specification and inspection methods: notions, challenges, and recent advancements.” The International Journal of Advanced Manufacturing Technology, pp. 1–12Google Scholar
  4. 4.
    AIAG (2002). “Measurement Systems Analysis. Reference Manual. 3rd Edition.”Automotive Industry Action GroupGoogle Scholar
  5. 5.
    Malamas EN, Petrakisa EGM, Zervakisa M, Petitb L, Legatb J-D (2003) A survey on industrial vision systems, applications, and tools. Image Vis Comput 21:171–188CrossRefGoogle Scholar
  6. 6.
    Yadong L, Peihua G (2004) Freeform surface inspection techniques state of the art review. CAD Comput Aided Des 36:1395–1417CrossRefGoogle Scholar
  7. 7.
    Ascione R, Polini W (2010) Measurement of nonrigid freeform surfaces by coordinate measuring machine. Int J Adv Manuf Technol 51:1055–1067CrossRefGoogle Scholar
  8. 8.
    Weckenmann A, Weickmann J (2006) Optical inspection of formed sheet metal parts applying fringe projection systems and virtual fixation. Metrol Meas Syst 13:321–334Google Scholar
  9. 9.
    A. E. Jaramillo, P. Boulanger, and F. Prieto (2009) “On- line 3-D inspection of deformable parts using FEM trained radial basis functions,” IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops, p. 1733–1739Google Scholar
  10. 10.
    Y. Caulier (2010) “Inspection of complex surfaces by means of structured light patterns,” vol. 18, pp. 6642–6660Google Scholar
  11. 11.
    Caulier Y, Bourennane S (2008) Fourier-based inspection of freeform reflective surfaces. Adv Concepts Intell Vis Syst Proc 5259:125–136CrossRefGoogle Scholar
  12. 12.
    Lin H-D, Chung C-Y, Lin W-T (2008) Principal component analysis based on wavelet characteristics applied to automated surface defect inspection. WSEAS Trans Comput Res 3:193–202Google Scholar
  13. 13.
    Cristea L, Manescu M (2008) Intelligent modular design of automatic dimensional inspection systems. WSEAS Trans Appl Theor Mech 3:739–748Google Scholar
  14. 14.
    Kase K, Makinouchi A, Nakagawa T, Suzuki H, Kimura F (1999) Shape error evaluation method of freeform surfaces. Comput Aided Des 31:495–505CrossRefzbMATHGoogle Scholar
  15. 15.
    Abenhaim GN, Tahan AS, Desrochers A, Maranzana R (2011) A novel approach for the inspection of flexible parts without the use of special fixtures. J Manuf Sci Eng: ASME 133:1–11CrossRefGoogle Scholar
  16. 16.
    Aidibe A, Tahan AS, Abenhaim GN (2012) Distinguishing profile deviations from a part’s deformation using the maximum normed residual test. WSEAS Trans Appl Theor Mech 7:18–28Google Scholar
  17. 17.
    Radvar-Esfahlan H, Tahan S-A (2012) Nonrigid geometric metrology using generalized numerical inspection fixtures. Precis Eng 36:1–9CrossRefGoogle Scholar
  18. 18.
    Thompson R (1985) A note on restricted maximum likelihood estimation with an alternative outlier model. J R Stat Soc Ser B Methodol 47:53–55Google Scholar
  19. 19.
    D. C. Hoaglin, F. Mosteller, and J. W. Tukey (1983) Understanding robust and exploratory data analysis: WileyGoogle Scholar
  20. 20.
    Besl PJ, McKay HD (1992) A method for registration of 3D shapes. IEEE Trans Pattern Anal Mach Intell 14:239–256CrossRefGoogle Scholar
  21. 21.
    Barber CB, Dobkin DP, Huhdanpaa H (1996) The quickhull algorithm for convex hulls. ACM Trans Math Softw 22:469–483CrossRefzbMATHMathSciNetGoogle Scholar
  22. 22.
    Peng J, Li Q, Jay Kuo C-C, Zhou M (2003) “Estimating Gaussian curvatures from 3D meshes,” Proc. SPIE 5007. Hum Vision Electron Imaging VIII 5007:270–280CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.Products, Processes and Systems Engineering Laboratory (P²SEL), Department of Mechanical Engineering, École de Technologie Supérieure (ÉTS)MontrealCanada

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