Angled Line Method for Measuring Continuously Distributed Strain in Sheet Bending

[+] Author and Article Information
Slawomir J. Swillo, Kaushik Iyer, S. Jack Hu

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2125

J. Manuf. Sci. Eng 128(3), 651-658 (Jan 08, 2006) (8 pages) doi:10.1115/1.2193544 History: Received September 01, 2004; Revised January 08, 2006

A new method and optical system have been developed to measure the strain distribution in sheet metal bending. The method relies on a simple pattern, i.e., a single line of certain width, or an area having a boundary line, marked on the sheet before deformation. The line traverses a width of the sheet metal at an angle. The sheet metal is deformed and an equivalent two-dimensional image of the line after deformation is obtained. By comparing the two-dimensional equivalent of the line after deformation with that before deformation, the strain on the surface of the deformed region is determined. Experiments using sheet metal flanging and hemming were conducted to verify the effectiveness and determine the limitation of the proposed method.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Typical patterns used in existing methods (grid and Moiré) for surface strain measurement: (a) grid pattern, (b) pattern of parallel lines, (c) circle pattern

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Figure 2

Geometrical model of the specimen and bending process: (a) specimen before deformation; (b) angle band properties: ◻, the angle band; D is the band thickness; (c) condition of bending process; (d) angled line after bending. R, radius of the curvature; ◻, the bending angle, t, specimen thickness; W, width; L, deformation width

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Figure 3

Detailed, schematic outline of the procedure for obtaining the deformation of the angled line due to bending: (a) deformed sheet, (b) unrolled deformed sheet

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Figure 4

Schematic of the apparatus and procedure for measuring the deformation of the angled line due to bending

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Figure 5

3D to 2D transformation of the deformed angled line

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Figure 6

Procedure for obtaining the strain distribution: (a) direct comparison of the un-deformed angled line with the unrolled deformed angled line, (b) displacement vector graph, (c) displacement function representation, (d) strain calculation for un-deformed and deformed coordinates system

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Figure 7

Schematic of the optical measurement system for sheet metal bending

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Figure 8

Image processing performed in the present study to demonstrate the ALM: (a) original image—selected area, (b) binary threshold and image correction, (c) border line determination

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Figure 9

ALM computation procedure: (a) 3D-to-2D conversion of boundary of the deformed angled line, (b) displacement determination and polynominal fitting, (c) engineering strain calculation

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Figure 10

Comparison of measured strain distributions obtained with the angled line method (ALM) and other (circle grid, line grid, square grid, and Moiré pattern)

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Figure 11

Repeatability test of the ALM algorithm. (a) Three specimens selected for the repeatability analysis, (b) results for the repeatability.

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Figure 12

Evaluation of ALM accuracy: (a) known function of the displacement, (b) angled line pattern generated based on function (a)

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Figure 13

Strain analysis based on a simulated deformed angled line: (a) strain distribution using measurement and theoretical calculation, (b) selected sections magnified, (c) error distribution




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