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Research Papers

Fractal Geometry Rooted Incremental Toolpath for Incremental Sheet Forming

[+] Author and Article Information
Harish K. Nirala

Department of Mechanical Engineering,
Indian Institute of Technology Ropar,
Rupnagar 140001, Punjab, India
e-mail: harish.nirala@iitrpr.ac.in

Anupam Agrawal

Department of Mechanical Engineering,
Indian Institute of Technology Ropar,
Rupnagar 140001, Punjab, India
e-mail: anupam@iitrpr.ac.in

1Corresponding author.

Manuscript received March 9, 2017; final manuscript received June 30, 2017; published online December 18, 2017. Assoc. Editor: Tony Schmitz.

J. Manuf. Sci. Eng 140(2), 021005 (Dec 18, 2017) (9 pages) Paper No: MANU-17-1139; doi: 10.1115/1.4037237 History: Received March 09, 2017; Revised June 30, 2017

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.

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Figures

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Fig. 1

Schematic representation of SPISF process

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Fig. 2

(a) Constant increment and (b) spiral increment toolpath shown using Matlab®

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Fig. 3

Hilbert-based fractal toolpath (orders 2–5)

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Fig. 4

Incremental toolpath (a) constant Z, (b) spiral incremental, and (c) FGBIT for square cup

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Fig. 5

Finite element model for SPISF

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Fig. 6

Incrementally formed square cup by numerical simulations using (a) spiral toolpath, (b) constant Z toolpath, and (c) FGBIT

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Fig. 7

Meridional stress distribution along x displacement direction

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Fig. 8

Direction of principal stresses at a point during deformation

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Fig. 9

(a) CAD model of fixture and (b) experimental setup

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Fig. 10

Formed square cup by (a) spiral toolpath, (b) constant Z toolpath, and (c) FGBIT

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Fig. 11

Thickness distribution with forming depth

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Fig. 12

von mises stress distribution along x displacement direction

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