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Research Papers

A New Model for the Prediction of Width Spread in Roughing Mills

[+] Author and Article Information
Dong Hoon Lee

Department of Mechanical Engineering,
POSTECH,
Pohang 790-784, South Korea
e-mail: wwffri@postech.ac.kr

Kyong Bo Lee

Department of Mechanical Engineering,
POSTECH,
Pohang 790-784, South Korea
e-mail: kyongbo@postech.ac.kr

Jae Sang Lee

Department of Mechanical Engineering,
POSTECH,
Pohang 790-784, South Korea
e-mail: Ljs5119@postech.ac.kr

Sung Jin Yun

Department of Mechanical Engineering,
POSTECH,
Pohang 790-784, South Korea
e-mail: sungjin@postech.ac.kr

Tae Jin Shin

Department of Mechanical Engineering,
POSTECH,
Pohang 790-784, South Korea
e-mail: tjshin@postech.ac.kr

Sang Moo Hwang

Department of Mechanical Engineering,
POSTECH,
Pohang 790-784, South Korea
e-mail: smhwang@postech.ac.kr

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received January 8, 2014; final manuscript received June 25, 2014; published online August 6, 2014. Assoc. Editor: Gracious Ngaile.

J. Manuf. Sci. Eng 136(5), 051014 (Aug 06, 2014) (9 pages) Paper No: MANU-14-1011; doi: 10.1115/1.4027970 History: Received January 08, 2014; Revised June 25, 2014

Abstract

Precision control of the slab width is crucial for product quality and production economy in roughing mill. In this paper, we present a new model for the prediction of the width spread of a slab during rolling in the roughing train of a hot strip mill. The approach is based on the extremum principle for rigid plastic materials, and applicable to horizontal rolling of a slab with either a dog-bone shaped cross section or a rectangular cross section. Also, the upper bound theorem is used for calculating the width spread of a slab. The prediction accuracy of the proposed model is examined through comparison with the predictions from the 3D finite element (FE) process simulations.

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Figures

Fig. 1

Width spread in a roughing train (top view)

Fig. 2

Definition sketch of flat rolling. Only a quadrant of the rolling geometry is shown.

Fig. 3

Change in the width of a small element in the bite zone, lateral spread, etc.

Fig. 4

A mathematical representation of a dog-bone shaped cross section. A1 represents the area above the line z = H1(0), A2 represents the area below the line z = H1(0), bp represents the distance from the edge to the peak, and hp represents the dog-bone height. For dog-bone profile I, an eighth order polynomial is used, while a fourth order polynomial is used for dog-bone profile II.

Fig. 5

FE simulation of width spread in flat rolling of a bar with the dog-bone shaped cross section. H1(0) = 40.675 mm, H2 = 28.473 mm, b = 142.363 mm, and R = 600 mm.

Fig. 6

Lateral displacements in the bite zone across the bar width. H1(0) = 62.5 mm, H2 = 50 mm, b = 570 mm, and R = 600 mm. Line no. 1 indicates the lateral displacement at the roll entrance, while line no. 10 indicates the lateral displacement at the roll exit. α1 = 3.9627 is used.

Fig. 7

Lateral displacements in the bite zone along the rolling direction. H1(0) = 62.5 mm, H2 = 50 mm, b = 570 mm, and R = 600 mm. Line no. 1 indicates the lateral displacement at the center of the bar, while line no. 10 indicates the lateral displacement at the edge. α1 = 3.9627 is used.

Fig. 8

Width spread for the problem of a dog-bone shaped inlet cross section. Comparison between predictions from the present model and those from FEM. The data represent change in the whole width (not half width) after rolling.

Fig. 9

The effect of dog-bone profile on width spread

Fig. 10

Width spread for the problem of a rectangular inlet cross section. Comparison between predictions from the present model (P(x) = Q(x)) and those from FEM. The data represents change in the whole width (not half width) after rolling.

Fig. 11

Lateral displacement in the bite zone along the rolling direction, predictions from FEM. H1 = 24.19 mm, H2 = 19.35 mm, and b = 84.66 mm. Line no. 1 indicates the lateral displacement at the roll entrance, while line no. 10 indicates the lateral displacement at the roll exit. α1 = 4.3314 and c = 2.165 is used.

Fig. 12

Lateral displacement in the bite zone along the rolling direction, Predictions from FEM. H1 = 24.19 mm, H2 = 19.35 mm, and b = 84.66 mm. Line no. 1 indicates the lateral displacement at the center, while line no. 10 indicates the lateral displacement at the edge of the slab. α1 = 4.3314 and c = 2.165 is used.

Fig. 13

Effect of s and r on c. γ = 3.5.

Fig. 14

c values, comparison between predictions from the proposed equation and those from FE simulation. The range of s: 0.75–1.75, the range of r: 0.1–0.3, and the range of γ: 3.5–13.5.

Fig. 15

Width spread for the problem of a rectangular inlet cross section. Comparison between predictions from the present model and those from FEM. The data represent change in the whole width (not half width) after rolling.

Fig. 16

Width spread for the problem of a rectangular inlet cross section. Comparison between predictions from the Shibahara model [6] and those from FEM. The data represent change in the whole width (not half width) after rolling.

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