International Journal of Material Forming

, Volume 9, Issue 3, pp 371–382 | Cite as

Optimization of relative tool position in accumulative double sided incremental forming using finite element analysis and model bias correction

  • Ebot Ndip-Agbor
  • Jacob Smith
  • Huaqing Ren
  • Zhen Jiang
  • Jiachen Xu
  • Newell Moser
  • Wei Chen
  • Z. Cedric Xia
  • Jian Cao
Thematic Issue: Flexible forming - Incremental Sheet Forming & Roll Forming

Abstract

Double-Sided Incremental Forming (DSIF) uses two small, independently moving, hemispherical tools on either side of the sheet to form a desired shape by following a predefined tool path. This study was motivated by the observation that the relative tool position of the tools, specified in the tool path generation algorithm, affects the formed geometric accuracy. A methodology for defining the relative tool positioning in the tool path generation algorithm based on local part geometry is proposed using simplified Finite Element Analysis (FEA) and sample physical experiments combined with Gaussian Process modeling techniques. This approach can take into account the mechanics of deformation in DSIF explicitly and physical compliance of the DSIF machine implicitly. Physical experiments were performed to demonstrate the effectiveness of the proposed framework.

Keywords

Incremental forming Process design Design methodology 

Nomenclature

D

the in-plane distance between the two tool axes

S

distance from top of bottom to bottom of the sheet

Δz

incremental depth

θdesired

desired wall angle

θformed

formed wall angle

rt

radius of top tool

rb

radius of bottom tool

t0

initial sheet thickness

References

  1. 1.
    Jeswiet J, Micari F, Hirt G, Bramley A, Duflou J, Allwood J (2005) Asymmetric single point incremental forming of sheet metal. CIRP Ann Manuf Technol 54(2):88–114. doi:10.1016/S0007-8506(07)60021-3 CrossRefGoogle Scholar
  2. 2.
    Allwood JM, Braun D, Music O (2010) The effect of partially Cut-out blanks on geometric accuracy in incremental sheet forming. J Mater Process Technol 210:1501–1510CrossRefGoogle Scholar
  3. 3.
    Allwood JM, Music O, Raithathna A, Duncan SR (2009) Closed-loop feedback control of product properties in flexible metal forming processes with mobile tools. CIRP Ann Manuf Technol 58(1):287–290. doi:10.1016/j.cirp.2009.03.065 CrossRefGoogle Scholar
  4. 4.
    Bambach M, Taleb Araghi B, Hirt G (2009) Strategies to improve the geometric accuracy in asymmetric single point incremental forming. Prod Eng 3(2):145–156. doi:10.1007/s11740-009-0150-8
  5. 5.
    Duflou JR, Verbert J, Belkassem B, Gu J, Sol H, Henrard C, Habraken AM (2008) Process window enhancement for single point incremental forming through multi-step toolpaths. CIRP Ann Manuf Technol 57(1):253–256. doi:10.1016/j.cirp.2008.03.030 CrossRefGoogle Scholar
  6. 6.
    Taleb Araghi B, Göttmann A, Bambach M, Hirt G, Bergweiler G, Diettrich J, Steiners M, Saeed-Akbarii A (2011) Review on the development of a hybrid incremental sheet forming system for small batch sizes and individualized production. Prod Eng 5(4):393. doi:10.1007/s11740-011-0325-y CrossRefGoogle Scholar
  7. 7.
    Behera AK, Lauwers B, Duflou JR (2014) Tool path generation framework for accurate manufacture of complex 3D sheet metal parts using single point incremental forming. Comput Ind 65(4):563–584. doi:10.1016/j.compind.2014.01.002 CrossRefGoogle Scholar
  8. 8.
    Göttmann A, Bailly D, Bergweiler G, Bambach M, Stollenwerk J, Hirt G, Loosen P (2012) Laser-assisted asymteric incremental sheet forming (laisf) of titanium sheet metal parts Sub- mitted in production engineering research and development. J: Int J Adv Manuf Technol. doi:10.1007/s00170-012-4640-z Google Scholar
  9. 9.
    Malhotra R, Cao J, Ren F, Kiridena V, Cedric Xia Z, Reddy NV (2011) “Improvement of geometric accuracy in incremental forming by using a squeezing toolpath strategy with two forming tools”. J Manuf Sci Eng 133(6):61019. doi:10.1115/1.4005179 CrossRefGoogle Scholar
  10. 10.
    Meier H, Magnus C, Smukala V (2011) “Impact of superimposed pressure on dieless incremental sheet metal forming with two moving tools”. CIRP Ann Manuf Technol 60(1):327–330. doi:10.1016/j.cirp.2011.03.134 CrossRefGoogle Scholar
  11. 11.
    Tekkaya AE, Shankar R, Sebastiani G, Homberg W, Kleiner M (2007) Surface reconstruction for incremental forming. Prod Eng Res Dev 1:71–78CrossRefGoogle Scholar
  12. 12.
    Malhotra R, Cao J, Beltran M, Xu D, Magargee J, Kiridena V, Xia ZC (2012) “Accumulative-DSIF strategy for enhancing process capabilities in incremental forming”. CIRP Ann Manuf Technol 61(1):251–254. doi:10.1016/j.cirp.2012.03.093 CrossRefGoogle Scholar
  13. 13.
    Kiridena V, Xia ZC (2010) A method of incrementally forming a workpiece, patent pendingGoogle Scholar
  14. 14.
    Jackson K, Allwood J (2009) The mechanics of incremental sheet forming. J Mater Process Technol 209(3):1158–1174. doi:10.1016/j.jmatprotec.2008.03.025 CrossRefGoogle Scholar
  15. 15.
    He S, Van Bael A, van Houtte P, Duflou JR, Szekeres A, Henrard C, Habraken AM (2005) “Finite element modeling of incremental forming of aluminum sheets”. Adv Mater Res 6–8:525–532. doi:10.4028/www.scientific.net/AMR. 6-8.525 CrossRefGoogle Scholar
  16. 16.
    Guzmán CF, Gu J, Duflou J, Vanhove H, Flores P, Habraken AM (2012) Study of the geometrical inaccuracy on a SPIF two-slope pyramid by finite element simulations. Int J Solids Struct 49(25):3594–3604. doi:10.1016/j.ijsolstr.2012.07.016 CrossRefGoogle Scholar
  17. 17.
    Ayed LB, Robert C, Delamézière A, Nouari M, Batoz JL (2014) Simplified numerical approach for incremental sheet metal forming process. Eng Struct 62–63:75–86. doi:10.1016/j.engstruct.2014.01.033 CrossRefGoogle Scholar
  18. 18.
    Lu B, Chen J, Ou H, Cao J (2013) “Feature-based tool path generation approach for incremental sheet forming process”. J Mater Process Technol 213(7):1221–1233. doi:10.1016/j.bbr.2011.03.023 CrossRefGoogle Scholar
  19. 19.
    Smith J, Malhotra R, Liu WK, Cao J (2013) “Deformation mechanics in single-point and accumulative double-sided incremental forming”. London: Int J Adv Manuf Technol 69(5-8):1185–1201. doi:10.1007/s00170-013-5053-3
  20. 20.
    Arendt PD, Apley DW, Chen W (2012) “Quantification of model uncertainty: calibration, model discrepancy, and identifiability”. J Mech Des 134(10):100908. doi:10.1115/1.4007390 CrossRefGoogle Scholar
  21. 21.
    Higdon D, Kennedy M, Cavendish JC, Cafeo JA et al (2004) “Combining field data and computer simulations for calibration and prediction”. Siam J Sci Comput 26(2):448–466. doi:10.1137/S1064827503426693 MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Jiang Z, Chen W, Fu Y, Yang R (2013) Reliability-based design optimization with model bias and data uncertainty. SAE Int J Mater Manuf 6(3):502–516. doi:10.4271/2013-01-1384 CrossRefGoogle Scholar
  23. 23.
    Kennedy MC, O’Hagan A (2001) Bayesian calibration of computer models. J R Stat Soc Ser B (Stat Methodol) 63(3):425–464MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Liu F, Bayarri MJ, Berger JO, Paulo R et al (2008) “A Bayesian analysis of the thermal challenge problem”. Comput Methods Appl Mech Eng 197(29–32):2457–2466. doi:10.1016/j.cma.2007.05.032 CrossRefMATHGoogle Scholar
  25. 25.
    Meier H, Buff B, Laurischkat R, Smukala V (2009) Increasing the part accuracy in dieless robot-based incremental sheet metal forming. CIRP Ann Manuf Technol 58(1):233–238. doi:10.1016/j.cirp.2009.03.056 CrossRefGoogle Scholar
  26. 26.
    Meier H, Magnus C, Smukala V (2011) Impact of superimposed pressure on dieless incremental sheet metal forming with two moving tools. CIRP Ann Manuf Technol 60(1):327–330. doi:10.1016/j.cirp.2011.03.134 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag France 2015

Authors and Affiliations

  • Ebot Ndip-Agbor
    • 1
  • Jacob Smith
    • 1
  • Huaqing Ren
    • 1
  • Zhen Jiang
    • 1
  • Jiachen Xu
    • 1
  • Newell Moser
    • 1
  • Wei Chen
    • 1
  • Z. Cedric Xia
    • 2
  • Jian Cao
    • 1
  1. 1.Northwestern UniversityEvanstonUSA
  2. 2.Ford Motor CompanyDearbornUSA

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