Advertisement

Investigating the design and process parameters of folded perforated sheet metal

  • Muhammad Ali Ablat
  • Ala QattawiEmail author
ORIGINAL ARTICLE
  • 31 Downloads

Abstract

Origami-based sheet metal (OSM) bending is an extension of rigid origami technique, where the final 3D structure is created from a single 2D flat pattern by bending. The key aspect of OSM is material discontinuity (MD), which helps achieve a unique dieless bending process. MD is a feature along bend line of blank sheet and it can be fabricated using laser or water jet cutting. Even though a number of successful implementations of OSM bending have been found, these cases are limited only to product development and industrial application. The mechanics of OSM bending with respect to parameters that define MD, blank sheet, as well as the bending process have not been studied. Thus, this study identifies parameters and investigates the effect of identified parameters associated with OSM bending. Parameters studied in this work include design parameters and process parameters. Design parameters are kerf-to-thickness (k/t) ratio, web-to-width (w/b) ratio, and thickness of sheet (t). These are associated with MD design. The process parameters are related to OSM bending process, and they include punch placement (t+g), offset distance (s), and punch radius (RP). Finite element analysis (FEA) is performed to investigate the effect of these parameters on the OSM bending process. The simulated OSM bending cases resulted in successful bending without using a die. The general recommendation is provided for selecting parameters of OSM bending based on results. In addition, the shape of MD is an important factor when designing the OSM bending process.

Keywords

Perforated sheet metal Origami-based sheet metal Folded metal Material discontinuities Sheet manufacturing Kerf 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Funding

This work was partially funded by the Hellman Faculty Fund-No 55253.

References

  1. 1.
    Tachi T (2011) Rigid-foldable thick origami. Origami 5 Fifth Int Meet Origami Sci Math Educ:253–264Google Scholar
  2. 2.
    Wu W, You Z (2011) A solution for folding rigid tall shopping bags. Proc R Soc 467:2561–2574.  https://doi.org/10.1098/rspa.2011.0120 MathSciNetCrossRefGoogle Scholar
  3. 3.
    Lang RJ, Nelson T, Howell L, Magleby S. Thick rigidly foldable origami mechanisms. ASME 2016 Int Des Eng Tech.Conf Comput Inf Eng Conf, 2016, p. 1–20.Google Scholar
  4. 4.
    Hull T. Project origami: activities for exploring mathematics. Second Edi. CRC Press; 2012.Google Scholar
  5. 5.
    Demaine ED, Rourke JO. Geometric folding algorithms: linkages, origami, polyhedra. Cambridge: Cambridge University Press; 2007.Google Scholar
  6. 6.
    Tolman KA, Merriam EG, Howell LL (2016) Compliant constant-force linear-motion mechanism. Mech Mach Theory 106:68–79.  https://doi.org/10.1016/j.mechmachtheory.2016.08.009 CrossRefGoogle Scholar
  7. 7.
    De Temmerman N. Design and analysis of deployable bar structures for mobile architectural applications. Vrije Universiteit Brussel, 2007Google Scholar
  8. 8.
    Morgan J, Magleby SP, Howell LL (2016) An approach to designing origami-adapted aerospace mechanisms. J Mech Des 138:052301.  https://doi.org/10.1115/1.4032973 CrossRefGoogle Scholar
  9. 9.
    Shi Q, Shi X, Gattas JM, Kitipornchai S (2017) Folded assembly methods for thin-walled steel structures. J Constr Steel Res 138:235–245.  https://doi.org/10.1016/j.jcsr.2017.07.010 CrossRefGoogle Scholar
  10. 10.
    Cheung KC, Tachi T, Calisch S, Miura K (2014) Origami interleaved tube cellular materials. Smart Mater Struct 23:1–10.  https://doi.org/10.1088/0964-1726/23/9/094012 CrossRefGoogle Scholar
  11. 11.
    Silverberg JL, Evans AA, McLeod L, Hayward RC, Hull T, Santangelo CD, Cohen I (2014) Using origami design principles to fold reprogrammable mechanical metamaterials. Sci (80- ) 345:647–650CrossRefGoogle Scholar
  12. 12.
    Nishiyama Y (2012) Miura folding: applying origami to space exploration. Int J Pure Appl Math 79:269–279zbMATHGoogle Scholar
  13. 13.
    Yao S, Liu X, Georgakopoulos SV, Tentzeris MM (2014) A novel reconfigurable origami spring antenna. IEEE Antennas Propag. Soc. AP-S Int. Symp., Memphis, USA: IEEE Press:374–375.  https://doi.org/10.1109/APS.2014.6904519
  14. 14.
    Max W. Durney A. D. Pendley Precision-folded, high strength, fatigue-resistant structures and sheet therefor. US 8,377,566 B2, 2013Google Scholar
  15. 15.
    Gitlin B, Kveton A, Lalvani J. Method of bending sheet metal to form three-dimensional sturctures. US 6,640,605 B2, 2002.Google Scholar
  16. 16.
    Gupta SK, Bourne DA, Kim KH, Krishnan SS (1998) Automated process planning for sheet metal bending operations. J Manuf Syst 17:338–360.  https://doi.org/10.1016/S0278-6125(98)80002-2 CrossRefGoogle Scholar
  17. 17.
    Ali Ablat M, Qattawi A (2018) Finite element analysis of origami-based sheet metal folding process. J Eng Mater Technol 140:1–8.  https://doi.org/10.1115/1.4039505 CrossRefGoogle Scholar
  18. 18.
    Durney MW. Precision-folded, high strength, fatigue-resistant structures and sheet therefor. US 2006/0207212 A1, 2006Google Scholar
  19. 19.
    Qattawi A, Mayyas A, Omar MA (2013) An investigation of graph traversal algorithms in folded sheet metal parts design. Int J Adv Manuf Technol 69:2237–2246.  https://doi.org/10.1007/s00170-013-5181-9 CrossRefGoogle Scholar
  20. 20.
    Abel Z, Connelly R, Demaine ED, Demaine ML, Hull TC, Lubiw A et al (2014) Rigid flattening of polyhedra with slits. Abstr. from 6th Int. Meet. Origami Sci. Math. Educ. (OSME 2014), Tokyo, Japan:1–10Google Scholar
  21. 21.
    Shpitalni M, Lipson H (2000) 3D conceptual design of sheet metal products by sketching. J Mater Process Technol 103:128–134.  https://doi.org/10.1016/S0924-0136(00)00400-3 CrossRefGoogle Scholar
  22. 22.
    Qattawi A. Optimizing Origami-based sheet metal parts using traversal algorithms and manufacturing based indices. Proc ASME 2016 Int. Manuf. Sci. Eng. Conf. MSEC2016 June 27–July 1, 2016 Blacksburg, USA, Blacksburg, Virginia,: 2016, p. 1–7.  https://doi.org/10.1115/MSEC2016-8754.
  23. 23.
    Venhovens P, Bell K, Marathe P, Patkar A, Lamance F, Lind D et al (2013) Application of a novel metal folding technology for automotive BiW design. SAE Int J Passeng Cars - Mech Syst 6:584–600.  https://doi.org/10.4271/2013-01-0373 CrossRefGoogle Scholar
  24. 24.
    Turner N, Goodwine B, Sen M (2015) A review of origami and its applications in mechanical engineering. J Mech Eng Sci 0:1–18.  https://doi.org/10.1177/0954406215597713 CrossRefGoogle Scholar
  25. 25.
    Lebée A (2015) From folds to structures, a review. Int J Sp Struct 30:55–75CrossRefGoogle Scholar
  26. 26.
    Schenk M, Viquerat AD, Seffen KA, Guest SD (2014) Review of inflatable booms for deployable space structures : packing and rigidization. J Spacecr Rocket 51:762–778.  https://doi.org/10.2514/1.A32598. CrossRefGoogle Scholar
  27. 27.
    Tang Y, Lin G, Yang S, Yi YK, Kamien RD, Yin J (2017) Programmable kiri-kirigami metamaterials. Adv Mater 29.  https://doi.org/10.1002/adma.201604262
  28. 28.
    Huffman DA (1976) Curvature and creases: a primer on paper. IEEE Trans Comput C-25:1010–1019.  https://doi.org/10.1109/TC.1976.1674542 CrossRefzbMATHGoogle Scholar
  29. 29.
    Miura K (1989, Ferrara, Italy: nd) A note to intrinsic geometry of origami. 1st Int Meet Origami Sci Technol:239–249Google Scholar
  30. 30.
    Belcastro S-M, Hull TC (2002) Modelling the folding of paper into three dimensions using affine transformations. Linear Algebra Appl 348:273–282.  https://doi.org/10.1016/S0024-3795(01)00608-5 MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Belcastro S-M, Hull TCA (2002) Mathematical model for non-flat origami. In: Hull T (ed) Origami 3, A K Peters. CRC Press, pp 39–51.  https://doi.org/10.1201/b15735-6
  32. 32.
    Tachi T (2009) Simulation of rigid origami. In: Origami 4, pp 175–187.  https://doi.org/10.1201/b10653-20 CrossRefGoogle Scholar
  33. 33.
    Tachi T. FreeForm Origami. Komaba, Tokyo, Japan: TSG, University of Tokyo College of Arts and Science,; 2010Google Scholar
  34. 34.
    Wu BW, You Z (2015) Modelling rigid origami with quaternions and dual quaternions. Proc R Soc 466:2155–2174.  https://doi.org/10.1098/rspa.2009.0625. MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Schenk M, Guest SD. Origami folding: a structural engineering approach 2011:1–16Google Scholar
  36. 36.
    Xi Z, Lien J. Folding rigid origami with closure constraints. Proc. ASME 2014 Int. Des. Eng. Tech. Conf. Comput. Inf. Eng. Conf. IDETC/CIE 2014 August 17–20, 2014, Buffalo, New York, USA, 2016, p. 2–11.Google Scholar
  37. 37.
    Zhou X, Wang H, You Z (2015) Design of three-dimensional origami structures based on a vertex approach. Proc R Soc A Math Phys Eng Sci 471:20150407.  https://doi.org/10.1098/rspa.2015.0407 CrossRefGoogle Scholar
  38. 38.
    Peraza Hernandez EA, Hartl DJ, Lagoudas DC. Kinematics of origami structures with smooth folds. J Mech Robot 2016;8:061019–061011–22.  https://doi.org/10.1115/1.4034299
  39. 39.
    Hoberman CS (1988) Reversibly expandable three dimensional structure. US 4:780,344Google Scholar
  40. 40.
    Trautz M, Kunstler A. Deployable folded plate structures—folding patterns based on 4-fold-mechanism using stiff plates. Proc Int Assoc Shell Spat Struct. Symp., Valencia, Spain: 2009, p. 2306–2317.Google Scholar
  41. 41.
    Hoberman C. Folding structures made of thick hinged sheets. US 7,794,019 B2, 2010Google Scholar
  42. 42.
    Zirbel SA, Lang RJ, Thomson MW, Sigel DA, Walkemeyer PE, Trease BP, Magleby SP, Howell LL (2013) Accommodating thickness in origami-based deployable arrays. J Mech Des 135:111005.  https://doi.org/10.1115/1.4025372. CrossRefGoogle Scholar
  43. 43.
    Abel Z, Cantarella J, Demaine ED, Eppstein D, Hull TC, Ku JS et al (2016) Rigid origami vertices: conditions and forcing sets. J Comput Geom 7:171–184.  https://doi.org/10.20382/jocg.v7i1a9. MathSciNetCrossRefzbMATHGoogle Scholar
  44. 44.
    Chen Y, Peng R, You Z. Origami of thick panels. Science (80- ) 2015;349:396–400.  https://doi.org/10.1126/science.aab2870.
  45. 45.
    Edmondson BJ, Lang RJ, Howell LL (2014) An offset panel technique for thick rigidily foldable origami. ASME 2014 Int. des. Eng. Tech. Conf. Comput. Inf. Eng. Conf. IDETC/CIE 2014, New York, USA:1–8Google Scholar
  46. 46.
    Ku JS, Demaine ED (2016) Folding flat crease patterns with thick materials. J Mech Robot 8:1–6.  https://doi.org/10.1115/1.4031954 CrossRefGoogle Scholar
  47. 47.
    Crampton EB, Magleby SP, Howell LL. Realizing origami mechanism from metal sheets. ASME 2017 Int. des. Eng. Tech. Conf. Comput. Inf. Eng. Conf. IDETC/CIE 2017, Cleveland, USA: 2017, p. 1–10Google Scholar
  48. 48.
    Cannella F, Dai JS. Origami-carton tuck-in with a reconfigurable linkage. ASME/IFToMM Int. Conf. Reconfigurable Mech. Robot., London, UK: Red Hook; 2009, p. 512–520.Google Scholar
  49. 49.
    Moon I, Do NAD, Konings R (2013) Foldable and standard containers in empty container repositioning. Transp Res Part E Logist Transp Rev 49:107–124.  https://doi.org/10.1016/j.tre.2012.07.005 CrossRefGoogle Scholar
  50. 50.
    Konings R, Thijs R (2001) Foldable containers: a new perspective on reducing container-repositioning costs technological, logistic and economic issues. Eur J Transp Infrastruct Res EJTIR 4:333–352Google Scholar
  51. 51.
    Yao S, Liu X, Georgakopoulos SV, Tentzeris MM (2014) A novel tunable origami accordion antenna. IEEE Antennas Propag Soc AP-S Int Symp, Memphis, USA: IEEE Press:370–371.  https://doi.org/10.1109/APS.2014.6904517
  52. 52.
    Willis AM. Collapsible kayak. US 2011/0017121 A1, 2011. US 2010/0311130 Al.Google Scholar
  53. 53.
    Song Z, Ma T, Tang R, Cheng Q, Wang X, Krishnaraju D, Panat R, Chan CK, Yu H, Jiang H (2014) Origami lithium-ion batteries. Nat Commun 5:1–6.  https://doi.org/10.1038/ncomms4140. CrossRefGoogle Scholar
  54. 54.
    Pesenti M, Masera G, Fiorito F, Sauchelli M (2015) Kinetic solar skin: a responsive folding technique. Energy Procedia 70:661–672.  https://doi.org/10.1016/j.egypro.2015.02.174 CrossRefGoogle Scholar
  55. 55.
    Boiko I. Building constructions made of perforated metallic materials. 4th Int. Sci. Conf. Civ Eng 13, Jelgava, LATVIA: 2013, p. 53–59.Google Scholar
  56. 56.
    C SK, Walame PMV (2016) Structural analysis for optimization of stairs in off road agricultural machinery. SSRG Int J Mech Eng 3:35–38Google Scholar
  57. 57.
    Komur MA (2011) Elasto-plastic buckling analysis for perforated steel plates subject to uniform compression. Mech Res Commun 38:117–122.  https://doi.org/10.1016/j.mechrescom.2011.01.001 CrossRefzbMATHGoogle Scholar
  58. 58.
    Kumar MM, S R, H Y, R YB. Study on effect of stress concentration on cutout orientation of plates with various cutouts and bluntness. Int J Ocean Syst Eng 2013;3:295–1303.  https://doi.org/10.5574/IJOSE.2011.1.2.095., Effect of Cutout Orientation on Stress Concentration of Perforated Plates with Various Cutouts and Bluntness
  59. 59.
    Saraçoğlu MH, Albayrak U (2016) Linear static analysis of perforated plates with round and staggered holes under their self-weights. Eng Struct Mater 2:39–47Google Scholar
  60. 60.
    Isoldi LA, De Real MV, Vaz J, Correia ALG, Dos Santos ED, Rocha LAO (2012) Numerical analysis of perforated thin plates subjected to tension or buckling. Proc - 2012 Int. Conf. Offshore Mar. Technol. Sci. Innov. NAVTEC 2012:46–49.  https://doi.org/10.1109/NAVTEC.2012.11
  61. 61.
    Khatam H, Pindera MJ (2011) Plastic deformation modes in perforated sheets and their relation to yield and limit surfaces. Int J Plast 27:1537–1559.  https://doi.org/10.1016/j.ijplas.2010.10.004 CrossRefzbMATHGoogle Scholar
  62. 62.
    Khatam H, Chen L, Pindera M-J. Elastic and plastic response of perforated metal sheets with different porosity architectures. J Eng Mater Technol 2009;131:031015–031011–14.  https://doi.org/10.1115/1.3086405.
  63. 63.
    Jia S, Raiser GF, Povirk GL (2002) Modeling the effects of hole distribution in perforated aluminum sheets I: representative unit cells. Int J Solids Struct 39:2533–2545.  https://doi.org/10.1016/S0020-7683(02)00115-4 CrossRefzbMATHGoogle Scholar
  64. 64.
    Baik SC, Kyu Hwan O, Lee DN (1996) Analysis of the deformation of a perforated sheet under uniaxial tension. J Mater Process Technol 58:139–144.  https://doi.org/10.1016/0924-0136(95)02096-9 CrossRefGoogle Scholar
  65. 65.
    Maiorana E, Pellegrino C, Modena C (2009) Elastic stability of plates with circular and rectangular holes subjected to axial compression and bending moment. Thin-Walled Struct 47:241–255.  https://doi.org/10.1016/j.tws.2008.08.003 CrossRefGoogle Scholar
  66. 66.
    Patle BC, Bhope D V. Evaluation of stress concentration factors in plate with oblique hole 2012;2:28–32.Google Scholar
  67. 67.
    Woo J-H, Na W-B (2011) Effect of cutout orientation on stress concentration of perforated plates with various cutouts and bluntness. Int J Ocean Syst Eng 1:95–101.  https://doi.org/10.5574/IJOSE.2011.1.2.095 CrossRefGoogle Scholar
  68. 68.
    Rezaeepazhand J, Jafari M (2010) Stress analysis of composite plates with a quasi-square cutout subjected to uniaxial tension. J Reinf Plast Compos 29:2015–2026.  https://doi.org/10.1177/0731684409341758 CrossRefGoogle Scholar
  69. 69.
    Louhghalam A, Igusa T, Park C, Choi S, Kim K (2011) Analysis of stress concentrations in plates with rectangular openings by a combined conformal mapping - finite element approach. Int J Solids Struct 48:1991–2004.  https://doi.org/10.1016/j.ijsolstr.2011.03.005 CrossRefGoogle Scholar
  70. 70.
    Liu J, Sun S, Guan Y (2009) Numerical investigation on the laser bending of stainless steel foil with pre-stresses. J Mater Process Technol 209:1580–1587.  https://doi.org/10.1016/j.jmatprotec.2008.04.006 CrossRefGoogle Scholar
  71. 71.
    Nandagopan OR, Ranjith Kumar S, Rajesh MR, Manoharan K, Nandakumar CG (2012) Nonlinear behaviour of perforated plate with lining. Def Sci J 62:248–251.  https://doi.org/10.14429/dsj.62.927 CrossRefGoogle Scholar
  72. 72.
    Bynum DJ, Lemcoe MM (1963) Birefringent-coating analysis of laterally loaded perforated plates. Exp Mech 3:140–147CrossRefGoogle Scholar
  73. 73.
    Ajudia CD, Dangar R, Jaykumar N (2016) Kothari DKD. A review paper on forming process of a review paper on forming process of perforated sheet. Int J Educ Sci Res Rev 3:1–8Google Scholar
  74. 74.
    Nakayama Y, Kodama A, Nagaki S, Abe T. FEM analysis on elastic-plastic deformation of perforated sheets. Met Mater 1998;4:319–321.Google Scholar
  75. 75.
    Elangovan K, Sathiya Narayanan C, Narayanasamy R (2010) Modelling of forming limit diagram of perforated commercial pure aluminium sheets using artificial neural network. Comput Mater Sci 47:1072–1078.  https://doi.org/10.1016/j.commatsci.2009.12.016 CrossRefGoogle Scholar
  76. 76.
    Elangovan K, Narayanan CS, Narayanasamy R (2011) Modelling the correlation between the geometrical features and the forming limit strains of perforated Al 8011 sheets using artificial neural network. Int J Mater Form 4:389–399.  https://doi.org/10.1007/s12289-010-1003-x CrossRefGoogle Scholar
  77. 77.
    Farsi MA, Arezoo B (2011) Bending force and spring-back in v-die-bending of perforated sheet-metal components. J Brazilian Soc Mech Sci Eng 33:45–51.  https://doi.org/10.1590/S1678-58782011000100007 CrossRefGoogle Scholar
  78. 78.
    Nasrollahi V, Arezoo B (2012) Prediction of springback in sheet metal components with holes on the bending area, using experiments, finite element and neural networks. Mater Des 36:331–336.  https://doi.org/10.1016/j.matdes.2011.11.039 CrossRefGoogle Scholar
  79. 79.
    Senthilnathan N, Venkatachalam G, Satonkar NN (2014) A two stage finite element analysis of electromagnetic forming of perforated aluminium sheet metals. Procedia Eng 97:1135–1144.  https://doi.org/10.1016/j.proeng.2014.12.392 CrossRefGoogle Scholar
  80. 80.
    Kothari KD, Jhala RL (2015) Investigation and parametric analysis of steel perforated sheet metal (PSM) for optimum forming process. Int J Eng Res Africa 21:118–123.  https://doi.org/10.4028/www.scientific.net/JERA.21.118 CrossRefGoogle Scholar
  81. 81.
    Venkatachalam G, Kumar V, Narayanan S (2013) Finite element analysis of forming limits for stretch forming of perforated aluminium sheet metals. ARPN. J Eng Appl Sci 8:652–655Google Scholar
  82. 82.
    Akitaya H a., Mitani J, Kanamori Y, Fukui Y. Generating folding sequences from crease patterns of flat-foldable origami. ACM SIGGRAPH 2013 Posters - SIGGRAPH ‘13 2013:1.  https://doi.org/10.1145/2503385.2503407.
  83. 83.
    Lang RJ (2011) Origami design secrets: mathematical methods for an ancient art, second edition. Taylor & FrancisGoogle Scholar
  84. 84.
    Qattawi A. Extending origami technique to fold forming of sheet metal. PhD Dessertation. Clem2son University, 2012Google Scholar
  85. 85.
    Azimi M, Mirjavadi SS, Asli SA, Hamouda AMS (2017) Fracture analysis of a special cracked lap shear (CLS) specimen with utilization of virtual crack closure technique (VCCT) by finite element methods. J Fail Anal Prev 17:304–314.  https://doi.org/10.1007/s11668-017-0243-1 CrossRefGoogle Scholar
  86. 86.
    Azimi M, Mirjavadi SS, Asli SA (2016) Investigation of mesh sensitivity influence to determine crack characteristic by finite element methods. J Fail Anal Prev 16:506–512.  https://doi.org/10.1007/s11668-016-0117-y CrossRefGoogle Scholar
  87. 87.
    Mirahmadi H, Azimi M, Mirjavadi SS (2016) Calculation of stress intensity factor for functionally graded cylinders with two radial cracks using the weight function method. Theor Appl Fract Mech 85:447–456.  https://doi.org/10.1016/j.tafmec.2016.06.004. CrossRefGoogle Scholar
  88. 88.
    Wagoner RH, Wang NM (1979) An experimental and analytical investigation of in-plane deformation of 2036-T4 aluminum sheet. Int J Mech Sci 21:255–264.  https://doi.org/10.1016/0020-7403(79)90001-8 CrossRefGoogle Scholar
  89. 89.
    Noori H, Mahmudi R (2007) Prediction of forming limit diagrams in sheet metals using different yield criteria. Metall Mater Trans A Phys Metall Mater Sci 38(A):2040–2052.  https://doi.org/10.1007/s11661-007-9239-x CrossRefGoogle Scholar
  90. 90.
    Pourboghrat F, Karabin ME, Becker RC, Chung K (2000) Hybrid membrane/shell method for calculating springback of anisotropic sheet metals undergoing axisymmetric loading. Int J Plast 16:677–700.  https://doi.org/10.1016/S0749-6419(99)00067-4. CrossRefzbMATHGoogle Scholar
  91. 91.
    Nourollahi GA, Farahani M, Babakhani A, Mirjavadi SS (2013) Compressive deformation behavior modeling of AZ31 magnesium alloy at elevated temperature considering the strain effect. Mater Res 16:1309–1314.  https://doi.org/10.1590/S1516-14392013005000149 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentUniversity of California, MercedMercedUSA
  2. 2.Mechanical, Industrial, & Manufacturing DepartmentUniversity of ToledoToledoUSA

Personalised recommendations