Slab analysis based on stream function method in chamfer edge rolling of ultra-heavy plate

Abstract

In this paper, three-dimensional velocity field is proposed by means of stream function method with bisecting yield criterion in chamfer edge rolling of ultra-heavy plate. Parabolic dog-bone shape function is derived so as to obtain velocity field with fixed angle of chamfer edge by stream function method, dog-bone shape coefficient η can be derived from volume invariant condition, and then the plastic deformation power, shear power as well as friction power are obtained respectively with the bisecting yield criterion. Summing up the power contributions, total power functional is presented, from which minimum value can be obtained by searching method, and vertical rolling force and torque are also finally obtained. The predictions of roll force and torque are compared with different angles of chamfer edge as well as different plate thicknesses. The results are shown to be in a very good agreement with the analytical and experimental results.

Keywords

Chamfer edge rolling parabolic dog-bone shape function stream function method velocity field bisecting yield criterion

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References

Tazoe N, Honjyo H, Takeuchi M, et al. New forms of hot strip mill width rolling installations. In: AISE spring conference, Warrendale, PA, USA, 1984, pp.1128–1132.

Shibahara

Misaka

Kono

. Edger set-up model at roughing train in hot strip mill. ISIJ Int 1981; 67: 2509–2509.

Ginzburg

. High-quality steel rolling theory and practice, New York: Marcel Dekker, 1993.

Okado

Ariizumi

Noma

. Width behavior of head and tail of slabs at edge rolling in hot strip mills. ISIJ Int 1981; 67: 2516–2516.

Liu

. Influences on the plastic strain distribution of slab of vertical roll shape during multi-pass V-H rolling process. Acta Metall Sin-Engl 2006; 19: 51–56.

Liu

Zhao

. FEM analysis for V-H rolling process by updating geometric method. J Mater Process Technol 2006; 180: 323–327.

Chun

Moon

. Optimization of the amount of edging to increase rolling yields in a plate mill. J Mater Process Technol 2000; 104: 11–16.

Yun

Lee

Kim

. A new model for the prediction of the dog-bone shape in steel mills. ISIJ Int 2012; 52: 1109–1117.

Abrinia

Fazlirad

. Investigation of single pass shape rolling using an upper bound method. J Mater Eng Perform 2008; 19: 541–552.

10.

Dvorkin

Goldschmit

Cavaliere

. 2D finite element parametric studies of the flat rolling process. J Mater Process Technol 1997; 68: 99–107.

11.

Xiong

Liu

Wang

. A three-dimensional finite element simulation of the vertical–horizontal rolling process in the width reduction of slab. J Mater Process Technol 2000; 101: 146–151.

12.

Zhao

Xie

Liu

. New yield equations based on geometric midline of error triangles between Tresca and twin shear stress yield loci. J Northeast Univ Nat Sci 2004; 25: 121–124.

13.

. Twin shear stress yield criterion. Int J Mech Sci 1983; 25: 71–74.

14.

Zhao

Xie

Liu

. Three-dimensional analysis of rolling by twin shear stress yield criterion. J Iron Steel Res Int 2006; 13: 21–26.

15.

Moon

Lee

. Approximate model for predicting roll force and torque in plate rolling with peening effect considered. ISIJ Int 2008; 48: 1409–1418.

16.

Zhao DW, Fang Q, Li CM, et al. Derivation of plastic specific work rate for equal area yield criterion and its application to rolling. J Iron Steel Res Int 2010; 17: 34–38.