Keywords: influence function method, work roll edge contact, rolling load, strip shape, thin strip, cold rolling.

Cold rolled thin strips have a wide application in both the electronic and instrument industries, and its production has always been of major interest to steel manufacturers. With the need for higher quality and productivity in cold strip mills, mathematical models of cold rolling of a strip with a desired shape and dimension, both for mill set-up and for on-line control, have become a key issue in the steel rolling process. One major part of these models concerns the strip and roll deformation, plastically deformed strip shape and profile. An influence function method analysis considering the strip plastic deformation and roll deformation can be directly used in the control of strip rolling, especially in the control of the shape and profile of the strip.

In practical rolling of thin strips, there is a phenomenon that the upper and lower work rolls may contact each other beyond the edges of strip if the strip is very thin and if there is no work roll bending system. This case often occurs during the thin strip rolling, and the rolled strip shape and profile will be affected significantly if the control model is not accurate. Roll edge contact forces between the upper and lower work rolls will change with different rolling conditions. The delivered thickness distribution of the strip depends on: the material properties; the reduction of the plastic deformation; the roll thermal and mechanical crown; the roll wear profile; the roll deformations due to the deflection of the rolls; the local contact effect which includes the flattening between the work roll and backup roll; the flattening between the work roll and strip and the edge contact of the work rolls. The edge contacts of the work rolls affect the deformation of the rolls and the strip shape, thus forming a new deformation feature in the cold rolling process. In this case, the models of deformation and mechanics are different from the traditional analysis of cold strip rolling. Not only will the distribution of the roll pressure change when the work rolls contact beyond the edges of the strip, but also the deformation model of work rolls [1], the friction variation at the interface of the rolls and the strip and work roll wear [2,3]. Le and Sutcliffe [4] developed a robust model for the rolling of a thin strip and foil and carried out experimental measurements of load and strip profiles. How to determine the distribution of rolling force and the strip shape and to find a method to improve its shape and profile when the work rolls contact beyond the strip edges are the new features of this study. The effects of the strip width and transverse friction on the roll edges contact length, the rolling force and strip shape have not been quantified before, which are discussed in the paper.

In this study, a modified semi-infinite body model was also introduced to calculate the flattening of the work roll-backup roll, and the work roll-strip. The Foppl model [5] was employed to simulate the edge contact between the upper and lower work rolls. Based on the theory of the slit beam, this special cold rolling of thin strip was calculated using an influence function method. A comparison of the forces and the strip shape with or without the work roll edge contact was carried out. The effect of the different rolling parameters, such as the reduction, strip width, friction coefficient and transverse friction distribution, on the mechanics and deformation of the cold rolling of thin strip were analysed. The model developed is useful to improve the shape and profile quality of thin strip in the cold rolling process. Based on the method developed, a comprehensive model which is suitable for simulating work roll edge contact can be obtained.

1

W.J. Edwards, P.D. Spooner, "Analysis of strip shape", in "Automation of Tandem Mills", G.F. Bryand (Editor), Iron and Steel Institute, London, 177-212, 1973.

2

J.G. Lenard, "The effect of lubricant additives on the coefficient of friction in cold rolling", J. Mater. Process. Technol., 80-81, 232-238, 1998. doi:10.1016/S0924-0136(98)00141-1

3

Z.Y. Jiang, A.K. Tieu, "A method to analyse the rolling of strip with ribs by 3-D rigid visco-plastic finite element method", J. Mater. Process. Technol., 117(1-2), 146-152, 2001. doi:10.1016/S0924-0136(01)01087-1

4

H.R. Le, M.P.F. Sutcliffe, "A robust model for rolling of thin strip and foil", Int. J. Mech. Sci., 43, 1405-1419, 2001. doi:10.1016/S0020-7403(00)00092-8

5

V.B. Ginzburg, M. Azzam, "Selection of optimum strip profile and flatness technology for rolling mills", Iron & Steel Engineer, 74(7), 30-38, 1997.

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