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TECHNICAL PAPERS

Fundamental Concepts for “Corner” Forming Limit Diagrams and Closed-Form Formulas for Planar Tube Hydroforming Analysis

[+] Author and Article Information
L. M. Smith, J. J. Caveney, T. Sun

 Oakland University, Rochester, MI 48309

J. Manuf. Sci. Eng 128(4), 874-883 (Dec 06, 2005) (10 pages) doi:10.1115/1.2280567 History: Received March 07, 2005; Revised December 06, 2005

A family of closed-form formulas for calculating minimum corner-fill radii in planar sections of tube hydroformed products is introduced. Corner forming limit diagrams relating the limiting major strain to the minimum corner-fill radius are introduced. The theory accounts for friction effects and accommodates regular shaped polygon die sections. This effort represents an exploration into a method for design and analysis of tube hydroforming processes without employing the finite element method and while using a closed form approach for capturing friction effects. Good agreement with experimental results is observed.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Example product design showing planes of analysis

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Figure 2

Corner-fill region decomposed into various segments

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Figure 3

Use and interpretation of C-FLD, where (R1>R2>R3>R4)

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Figure 4

C-FLD for square cross section for which the initial tube diameter is equal to the side length

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Figure 5

C-FLD for square cross section for which the initial tube diameter is equal to 90% of the side length

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Figure 6

C-FLD for square cross section for which the initial tube diameter is equal to 110% of the side length

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Figure 7

Quarter section of square die cross section analyzed using commercial finite element program, MARC

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Figure 8

Picture of the corner-fill tube final geometry. Specimen has been sectioned in half to expose cross section (from Auto/Steel Partnership (see Ref. 38).

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Figure 9

AKDQ-79 case with wet lubrication from Auto/Steel Partnership (see Ref. 38)

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Figure 10

AKDQ-79 case with dry lubrication from Auto/Steel Partnership (see Ref. 38)

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Figure 11

C-FLD for square cross section for which the initial tube diameter is equal to the side length. Experimental data superimposed upon proposed design envelope. For “Exper,” the initial tube diameter is equal to 0.938a. For “FEA” the initial tube diameter is equal to 0.953a.

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