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Research Papers

The Determination of Heating Shapes and Locations for Triangle Heating

[+] Author and Article Information
Young-Bum Kim

Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul 151-742, Koreainterac1@snu.ac.kr

Jung-Seo Park

Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul 151-742, Koreaemot97@snu.ac.kr

Jong-Gye Shin

 Research Institute of Marine Systems Engineering, Seoul 151-742, Koreajgshin@snu.ac.kr

Chung-Min Hyun

 Samsung Heavy Industries Co., Ltd., Geoje 656-710, Koreacm.hyun@samsung.com

Kwang-Hee Ko1

Department of Mechatronics, Gwangju Institute of Science and Technology, Gwangju 500-712, Koreakhko@gist.ac.kr

1

Corresponding author.

J. Manuf. Sci. Eng 131(2), 021007 (Mar 18, 2009) (12 pages) doi:10.1115/1.3090886 History: Received January 22, 2008; Revised January 02, 2009; Published March 18, 2009

Thermal forming is a method to form a curved plate by inducing local shrinkage and angular distortion through heating and cooling. In this approach, two different methods are available: line heating and triangle heating. Among them, this paper discusses triangle heating and presents algorithms for determining heating shapes and locations. The heating shape is determined by using the in-plane strain distributions, which are calculated by nonlinear kinematics analysis between the designed and initial shapes, field survey results, and mechanics based on the neutral axis. To predict the angular distortion and shrinkage in various heating conditions, a functional relation of residual deformations is formulated. For the formulation, multivariate analysis and multiple regression techniques are used with data obtained from experiments of unit triangle heating and numerical analysis. Using the determined heating shapes and the functional relation for the residual deformations, a correct triangle heating position is determined by an algorithm, which can predict qualitatively correct angular distortion and shrinkage in the interior and quantitatively correct distortion values on the edge. Finally, analytic verification of the proposed method has been done by applying the method to a convex type plate used in the field. The proposed work can be used for automation of curved plate fabrication in the shipyards.

Copyright © 2009 by American Society of Mechanical Engineers
Topics: Heating , Shapes , Deformation
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References

Figures

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Figure 1

Saddle (left) and convex (right) plates (12)

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Figure 2

Mechanism of triangle heating (11)

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Figure 3

The workflow for decision of heating conditions for triangle heating

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Figure 4

Various shapes of triangle heating areas

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Figure 5

A plate heated by a skillful field worker using the triangle heating method

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Figure 6

The diagram of a deformation of a flat plate in the xz coordinate plane (14)

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Figure 7

The in-plane strain distributions computed by the unfolding algorithm

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Figure 8

Calculation of an average in-plane strain distribution

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Figure 9

A parabolic surface

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Figure 10

The parabolic profile and the determination of the neutral axis

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Figure 11

The determined neutral axis

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Figure 12

Determination of the bottom length; the left figures are the in-plane strain distributions and the right ones are the heating areas

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Figure 13

A specimen for a unit triangle heating experiment

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Figure 14

The heating pattern used in the test

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Figure 15

The top view after heating

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Figure 16

HAZ XZ sections after unit triangle heating

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Figure 17

The numerical analysis result of the unit triangle heating (displacement z and scale factor of 20)

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Figure 18

Comparison of angular distortions: experiment versus numerical analysis

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Figure 19

Comparison of shrinkages: experiment versus numerical analysis

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Figure 20

The diagram to determine triangle heating locations

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Figure 21

The orientation of the triangle heating shapes with respect to the roll line; it is determined to be perpendicular to the roll line

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Figure 22

The designed plate

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Figure 23

The completed shape fabricated by a skillful field worker

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Figure 24

The shape and locations of heating areas for the triangle heating test with a real plate

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Figure 25

The numerical simulation result of the plate: (a) shows all the nodes used for analysis, (b) shows the nodes for one heating area, (c) shows the deformation in the z direction, and (d) shows the deformation in the z direction from a different view with a blown-up image in the corner

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Figure 26

The selected curves for comparison between the designed shape and the numerical simulation result

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