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Research Papers

Investigating Reliability of Variable Blank Holder Force Control in Sheet Drawing Under Process Uncertainties

[+] Author and Article Information
Wenfeng Zhang

Industrial, Welding and Systems Engineering, The Ohio State University, 1971 Neil Avenue, Columbus, OH 43210

Rajiv Shivpuri1

Industrial, Welding and Systems Engineering, The Ohio State University, 1971 Neil Avenue, Columbus, OH 43210shivpuri.1@osu.edu

1

Corresponding author.

J. Manuf. Sci. Eng 130(4), 041001 (Jul 08, 2008) (8 pages) doi:10.1115/1.2951936 History: Received December 08, 2005; Revised March 14, 2008; Published July 08, 2008

The blank holder force (BHF), which regulates the amount of metal drawn into the die cavity, has been used effectively to draw defect-free sheet parts. It has been shown that a properly designed variable BHF profile can provide greater drawability as compared to constant BHF. Extensive research has been carried out in the past to determine this optimal profile. However, these deterministic efforts neglect the sensitivity of this optimal BHF design to unintended process variations inherent in sheet forming. This paper investigates the reliability of optimal variable BHF in the presence of process uncertainties by minimizing the magnitude of wrinkling and fracture defects under probabilistic constraints. To demonstrate the efficacy of this approach, it analyzes the conical cup drawing of an aluminum killed deep-drawing quality steel under process uncertainties including sheet thickness, punch speed, interface friction at the punch surface, and interface friction at the die surface. The results show that probabilistic design improves the yield (probability of good parts) to 99.98% as compared to the 48.04% yield realized by the traditional deterministic design. In addition, Monte Carlo simulations verify that the probabilistic design handles the uncertainties better due to its inherent robustness. This is primarily due to the design moving away from the process constraints and at the same time balancing the probability of failure between the two failure modes.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Variation of input parameters and output quality features in the sheet drawing process with blank holder control

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Figure 2

Segmentation of design space in probabilistic formulation

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Figure 3

The blank holder control profile from Ref. 5 and the fitted Gaussian approximation for sheet drawing

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Figure 4

The FEM simulation model of the sheet drawing process and the final drawn part

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Figure 5

Maximum thinning and sidewall wrinkling (y-axis) at different s of BHF (x-axis)

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Figure 6

The design solution of the PI control, deterministic design, and probabilistic design for csw=0.21

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Figure 7

The design solution of the PI control, deterministic design, and probabilistic design for csw=0.23

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Figure 8

Histograms of sidewall wrinkling and maximum thinning for the deterministic and the probabilistic designs

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Figure 9

Thinning and sidewall wrinkling values (distributions) in the drawn cup for three cases: probabilistic design (near the mean), deterministic design, and probabilistic design 3sigma away from the mean.

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