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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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## References

McCrum, A. W., 1956, “Progress Report on the Experimental Investigation of Spread, Load, and Torque in Hot Flat Rolling,” BISRA Report MW/AL, Report No. 10/56.
Helmi, A., and Alexander, J. M., 1968, “Geometric Factors Affecting Spread in Hot Flat Rolling of Steel,” J. Iron Steel Inst., 206, pp. 1110–1117.
Beese, J. G., 1972, “Nomograms for Predicting the Spread of Hot Rolled Slabs,” AISE Yearly Proceedings, pp. 251–252.
Wusatowski, Z., 1955, “Hot Rolling: A Study of Draught, Spread and Elongation,” Iron Steel, 28, pp. 49–54.
El-Kalay, A. K. E. H. A., and Sparling, L. G. M., 1968, “Factors Affecting Friction and Their Effect Upon Load, Torque, and Spread in Hot Flat Rolling,” J. Iron Steel Inst., 206, pp. 152–163.
Shibahara, T., Misaka, Y., Kono, T., Koriki, M., and Takemoto, H., 1981, “Edger Set-Up Model at Roughing Train in Hot Strip Mill,” J. Iron Steel Inst. Jpn., 67, pp. 2509–2515.
Oh, S. I., and Kobayashi, S., 1975, “An Approximate Method for a Three-Dimensional Analysis of Rolling,” Int. J. Mech. Sci., 17, pp. 293–305.
Hill, R., 1963, “A General Method of Analysis for Metal-Working Processes,” J. Mech. Phys. Solids, 11, pp. 305–326.
Matsumoto, H., 1991, “2-Dimensional Lateral-Material-Flow Model Reduced From 3-Dimensional Theory for Flat Rolling,” ISIJ Int., 31, pp. 550–558.
Arora, J. S., 1989, Introduction to Optimum Design, McGraw-Hill, New York, Chap. 5.
Yun, D. J., Lee, D. H., Kim, J. B., and Hwang, S. M., 2012, “A New Model for the Prediction of the Dog-Bone Shape in Steel Mills,” ISIJ Int., 52, pp. 1109–1117.

## Figures

Fig. 1

Width spread in a roughing train (top view)

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. 3

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

Fig. 2

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

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. 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. 13

Effect of s and r on c. γ = 3.5.

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.

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. 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. 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. 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. 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.

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