Single point incremental sheet forming (SPISF) technique is an emerging process for die less forming. It has wide applications in many industries viz. automobile and medical bone transplants. Among several key parameters, toolpath planning is one of the critical aspects of SPISF. Also, formability and geometric accuracy have been the two major limitations in SPISF. Spiral and constant incremental toolpaths and their variants have been investigated in detail by several researchers. Fractal-based toolpath planning is also an attempt to improve the process of SPISF. Formability is measured in terms of thickness distribution and maximum forming depth achieved. This paper investigates a fractal geometry-based incremental toolpath (FGBIT) strategy to form a square cup using incremental sheet forming (ISF). Fractal toolpath is a space-filling toolpath which is developed by the fractal geometry theory. A comparison-based study is conducted to observe the benefits of using FGBIT over traditional toolpaths (spiral and constant Z). Better formability, stress, and thickness distribution have been observed by adopting the proposed toolpath strategy. This toolpath strategy is new in its kind and has not been investigated in the metal forming domain. Experiments and simulations are conducted to validate the concept with reasonable accuracy.
Issue Section:
Research Papers
References
1.
Young
, D.
, and Jeswiet
, J.
, 2004
, “Wall Thickness Variations in Single-Point Incremental Forming
,” Proc. Inst. Mech. Eng., Part B
, 218
(11
), pp. 1453
–1459
.2.
Jeswiet
, J.
, Micari
, F.
, Hirt
, G.
, Bramley
, A.
, Duflou
, J.
, and Allwood
, J.
, 2005
, “Asymmetric Single Point Incremental Forming of Sheet Metal
,” CIRP Ann. Manuf. Technol.
, 54
(2
), pp. 88
–114
.3.
Jackson
, K.
, and Allwood
, J.
, 2009
, “The Mechanics of Incremental Sheet Forming
,” J. Mater. Process. Technol.
, 209
(3
), pp. 1158
–1174
.4.
Leszak
, E.
, 1967
, “Apparatus and Process for Incremental Dieless Forming
,” U.S. Patent No. US3342051 A
.https://www.google.com/patents/US33420515.
Mason
, B.
, 1978
, “Sheet Metal Forming for Small Batches
,” Bachelor thesis, University of Nottingham, Nottingham, UK.6.
Matsubara
, S.
, 1994
, “Incremental Backward Bulge Forming of a Sheet Metal With a Hemispherical Head Tool-a Study of a Numerical Control Forming System II
,” J. Jpn. Soc. Technol. Plast.
, 35
(406), pp. 1311
–1311
.7.
Allwood
, J. M.
, Shouler
, D. R.
, and Tekkaya
, A. E.
, 2007
, “The Increased Forming Limits of Incremental Sheet Forming Processes
,” Key Engineering Materials
, Vol. 344
, Trans Tech Publications
, Zürich, Switzerland, pp. 621
–628
.8.
Duflou
, J. R.
, Verbert
, J.
, Belkassem
, B.
, Gu
, J.
, Sol
, H.
, Henrard
, C.
, and Habraken
, A. M.
, 2008
, “Process Window Enhancement for Single Point Incremental Forming Through Multi-Step Toolpaths
,” CIRP Ann. Manuf. Technol.
, 57
(1
), pp. 253
–256
.9.
Liu
, Z.
, Li
, Y.
, and Meehan
, P. A.
, 2013
, “Vertical Wall Formation and Material Flow Control for Incremental Sheet Forming by Revisiting Multistage Deformation Path Strategies
,” Mater. Manuf. Process
, 28
(5
), pp. 562
–571
.10.
Malhotra
, R.
, Bhattacharya
, A.
, Kumar
, A.
, Reddy
, N. V.
, and Cao
, J.
, 2011
, “A New Methodology for Multi-Pass Single Point Incremental Forming With Mixed Toolpaths
,” CIRP Ann. Manuf. Technol.
, 60
(1
), pp. 323
–326
.11.
Kim
, T. J.
, and Yang
, D. Y.
, 2000
, “Improvement of Formability for the Incremental Sheet Metal Forming Process
,” Int. J. Mech. Sci.
, 42
(7
), pp. 1271
–1286
.12.
Lu
, B.
, Chen
, J.
, Ou
, H.
, and Cao
, J.
, 2013
, “Feature-Based Tool Path Generation Approach for Incremental Sheet Forming Process
,” J. Mater. Process. Technol.
, 213
(7
), pp. 1221
–1233
.13.
Malhotra
, R.
, Reddy
, N. V.
, and Cao
, J.
, 2010
, “Automatic 3D Spiral Toolpath Generation for Single Point Incremental Forming
,” ASME J. Manuf. Sci. Eng.
, 132
(6
), p. 061003
.14.
Skjoedt
, M.
, Hancock
, M. H.
, and Bay
, N.
, 2007
, “Creating Helical Tool Paths for Single Point Incremental Forming
,” Key Engineering Materials
, Trans Tech Publications
, Zürich, Switzerland
, pp. 583
–590
.15.
Singh
, A.
, Nirala
, H. K.
, and Agrawal
, A.
, 2016
, “Investigations on Structural Thinning in Deformation Machining Stretching Mode
,” AIP Conf. Proc.
, 1769
(1
), p. 070017
.16.
Rose
, N. J.
, 2001
, “Hilbert-Type Space-Filling Curves
,” North Carolina State University
, Chicago, IL.http://www4.ncsu.edu/~njrose/pdfFiles/HilbertCurve.pdf17.
Cutting
, J. E.
, and Garvin
, J. J.
, 1987
, “Fractal Curves and Complexity
,” Atten. Percept. Psychophys.
, 42
(4
), pp. 365
–370
.18.
Shaikh
, S.
, Kumar
, N.
, Jain
, P. K.
, and Tandon
, P.
, 2016
, “Hilbert Curve Based Toolpath for FDM Process
,” CAD/CAM, Robotics and Factories of the Future
, Springer
, New Delhi, India
, pp. 751
–759
.19.
Kumar
, G. S.
, Pandithevan
, P.
, and Ambatti
, A. R.
, 2009
, “Fractal Raster Tool Paths for Layered Manufacturing of Porous Objects
,” Virtual Phys. Prototyping
, 4
(2
), pp. 91
–104
.20.
Mizugaki
, Y.
, Sakamoto
, M.
, and Sata
, T.
, 1992
, “Fractal Path Generation for a Metal-Mold Polishing Robot System and Its Evaluation by the Operability
,” CIRP Ann. Manuf. Technol.
, 41
(1
), pp. 531
–534
.21.
Cox
, J. J.
, Takezaki
, Y.
, Ferguson
, H. R.
, Kohkonen
, K. E.
, and Mulkay
, E. L.
, 1994
, “Space-Filling Curves in Tool-Path Applications
,” Comput. Aided Des.
, 26
(3
), pp. 215
–224
.22.
Mandelbrot
, B. B.
, and Pignoni
, R.
, 1983
, The Fractal Geometry of Nature
, Vol. 173
, WH Freeman
, New York
.23.
Chen
, C. C. A.
, Juang
, Y. S.
, and Lin
, W. Z.
, 2002
, “Generation of Fractal Toolpaths for Irregular Shapes of Surface Finishing Areas
,” J. Mater. Process. Technol.
, 127
(2
), pp. 146
–150
.24.
Ventrella
, J.
, 2012
, Brain Filling Curves—A Fractal Bestiary
, Lulu Press, Inc.
, Raleigh, NC
.25.
Lin
, W.
, Xu
, P.
, Li
, B.
, and Yang
, X.
, 2014
, “Path Planning of Mechanical Polishing Process for Freeform Surface With a Small Polishing Tool
,” Rob. Biomimetics
, 1
(1
), p. 24
.26.
Henrard
, C.
, 2009
, “Numerical Simulations of the Single Point Incremental Forming Process
,” Ph.D. dissertation
, The University of Liège, Liège, Belgium.http://bictel.ulg.ac.be/ETD-db/collection/available/ULgetd-04182009-184505/unrestricted/PhD_Henrard_Full.pdf27.
Nirala
, H. K.
, Jain
, P. K.
, Roy
, J. J.
, Samal
, M. K.
, and Tandon
, P.
, 2017
, “An Approach to Eliminate Stepped Features in Multistage Incremental Sheet Forming Process: Experimental and FEA Analysis
,” J. Mech. Sci. Technol.
, 31
(2
), pp. 599
–604
.28.
DASSAULT SYSTÈMES,
2012
, “Simulation of the Ballistic Perforation of Aluminum Plates With Abaqus/Explicit, Abaqus Technology Brief
,” DASSAULT SYSTÈMES, Waltham, MA.29.
Hirt
, G.
, Ames
, J.
, and Bambach
, M.
, 2005
, “A New Forming Strategy to Realize Parts Designed for Deep‐Drawing by Incremental CNC Sheet Forming
,” Steel Res. Int.
, 76
(2–3
), pp. 160
–166
.30.
Hadoush
, A.
, and Van den Boogaard
, A. H.
, 2008
, “Time Reduction in Implicit Single Point Incremental Sheet Forming Simulation by Refinement-Derefinement
,” Int. J. Mater. Form.
, 1
(Suppl. 1), pp. 1167
–1170
.31.
Petek
, A.
, Podgomik
, B.
, Kuzman
, K.
, Cekada
, M.
, Waldhauser
, W.
, and Vizintin
, J.
, 2008
, “The Analysis of Complex Tribological System of Single Point Incremental Sheet Metal Forming-SPIF
,” Strojniski Vestn.
, 54
(4
), pp. 266
–273
.http://cat.inist.fr/?aModele=afficheN&cpsidt=2039740232.
Corbett
, B. M.
, 2006
, “Numerical Simulations of Target Hole Diameters for Hypervelocity Impacts Into Elevated and Room Temperature Bumpers
,” Int. J. Impact Eng.
, 33
(1
), pp. 431
–440
.33.
Johnson
, G. R.
, and Cook
, W. H.
, 1985
, “Fracture Characteristics of Three Metals Subjected to Various Strains, Strain Rates, Temperatures and Pressures
,” Eng. Fract. Mech.
, 21
(1
), pp. 31
–48
.34.
Schwer
, L. E.
, and Windsor
, C. A.
, 2009
, “Aluminum Plate Perforation: A Comparative Case Study Using Lagrange With Erosion, Multi-Material ALE, and Smooth Particle Hydrodynamics
,” 7th European LS-DYNA Conference
, Salzburg, Austria, May 14–15.http://www.dynalook.com/european-conf-2009/J-I-01.pdf35.
Hancock
, J. W.
, and Mackenzie
, A. C.
, 1976
, “On the Mechanisms of Ductile Failure in High-Strength Steels Subjected to Multi-Axial Stress-States
,” J. Mech. Phys. Solids
, 24
(2–3
), pp. 147
–160
.36.
Rule
, W. K.
, and Jones
, S. E.
, 1998
, “A Revised Form for the Johnson–Cook Strength Model
,” Int. J. Impact Eng.
, 21
(8), pp. 609–624.37.
Hao
, S.
, and Brocks
, W.
, 1997
, “The Gurson-Tvergaard-Needleman-Model for Rate and Temperature-Dependent Materials With Isotropic and Kinematic Hardening
,” Comput. Mech.
, 20
(1
), pp. 34
–40
.38.
Xue
, L.
, 2008
, “Constitutive Modeling of Void Shearing Effect in Ductile Fracture of Porous Materials
,” Eng. Fract. Mech.
, 75
(11
), pp. 3343
–3366
.39.
Lemaitre
, J.
, 1985
, “A Continuous Damage Mechanics Model for Ductile Fracture
,” ASME J. Eng. Mater. Technol.
, 107
(1
), pp. 83
–89
.40.
Amaral
, R.
, Teixeira
, P.
, Azinpour
, E.
, Santos
, A. D.
, and de Sa
, J. C.
, 2016
, “Evaluation of Ductile Failure Models in Sheet Metal Forming
,” 12th International Conference on Numerical Methods in Industrial Forming Processes (NUMIFORM
), Rosières-près-Troyes, France, July 4–7, Vol. 80
, p. 03004
.41.
DASSAULT SYSTÈMES,
2002
, “ABAQUS Theory Manual Version 6.3
,” DASSAULT SYSTÈMES, Waltham, MA.42.
Banerjee
, A.
, Dhar
, S.
, Acharyya
, S.
, Datta
, D.
, and Nayak
, N.
, 2015
, “Determination of Johnson Cook Material and Failure Model Constants and Numerical Modelling of Charpy Impact Test of Armour Steel
,” Mater. Sci. Eng. A
, 640
, pp. 200
–209
.43.
Petek
, A.
, and Kuzman
, K.
, 2010
, “Prediction of Surface Stretches and Sheet Metal Thinning by Single Point Incremental Forming in Digital Environment
,” J. Technol. Plast.
, 35
(1–2
), pp. 1–9.http://www.dpm.ftn.uns.ac.rs/JTP/Download/2010/Article6.pdf44.
Bhattacharya
, A.
, Maneesh
, K.
, Reddy
, N. V.
, and Cao
, J.
, 2011
, “Formability and Surface Finish Studies in Single Point Incremental Forming
,” ASME J. Manuf. Sci. Eng.
, 133
(6
), p. 061020
.45.
Silva
, M. B.
, Skjoedt
, M.
, Atkins
, A. G.
, Bay
, N.
, and Martins
, P. A. F.
, 2008
, “Single‐Point Incremental Forming and Formability—Failure Diagrams
,” J. Strain Anal. Eng. Des.
, 43
(1
), pp. 15
–35
.46.
Fan
, J. P.
, Tang
, C. Y.
, Tsui
, C. P.
, Chan
, L. C.
, and Lee
, T. C.
, 2006
, “3D Finite Element Simulation of Deep Drawing With Damage Development
,” Int. J. Mach. Tools Manuf.
, 46
(9
), pp. 1035
–1044
.47.
Li
, J.
, Li
, S.
, Xie
, Z.
, and Wang
, W.
, 2015
, “Numerical Simulation of Incremental Sheet Forming Based on GTN Damage Model
,” Int. J. Adv. Manuf. Technol.
, 81
(9–12), pp. 2053–2065.48.
Sun
, J. S.
, Lee
, K. H.
, and Lee
, H. P.
, 2000
, “Comparison of Implicit and Explicit Finite Element Methods for Dynamic Problems
,” J. Mater. Process. Technol.
, 105
(1
), pp. 110
–118
.49.
Tekkaya
, A. E.
, 2000
, “State-of-the-Art of Simulation of Sheet Metal Forming
,” J. Mater. Process. Technol.
, 103
(1
), pp. 14
–22
.Copyright © 2018 by ASME
You do not currently have access to this content.
