Improved model to solve influence coefficients of work roll deflection

J. Cent. South Univ. Technol. (2010) 17: 1000−1005
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owing to a unit rolling force and a unit bending force. The influence coefficients for both rolling load and bending force were explicitly given out.
rolls may contact each other, which affects mechanics of asymmetrical rolling and crown of the rolled strip significantly. The traditional influence coefficient does not take account of this phenomenon, hence, it is not suitable to analyze the rolling process under this condition. JIANG et al [13−15] developed a modified influence function to study this special rolling problem. This model is effective and applicable in the cold rolling of thin strip with work roll edge contact. To calculate the influence coefficients of the rolls, SHOHET and TOWNSEND [3] treated the backup roll as a simply supported beam, the origin of the coordinate system was set at the center of the roll neck and the influence coefficient was denoted as the difference between the deflection at the origin and the point on the roll axis. However, the influence coefficient of work rolls was the same as that of backup. SHOHET and TOWNSEND gave no more explanations about it, and few literatures paid more attention to it. EDWARDS and SPOONER [4] improved SHOHET’s model, and different beam models were employed for backup roll and work roll in their work. Different expressions of the influence coefficients were obtained, but because of different coordinate systems and the expression form of influence coefficients, they cannot be applied directly to the program based on SHOHET’s model. In this study, a rational explanation for SHOHET’s model was provided by introducing a virtual bending force, and then, an improved model for work roll deflection was employed to deduce influence coefficients
Abstract: According to the concept of virtual bending force, a rational explanation for SHOHET’s model was presented. Considering the deformation characters of the work rolls in four-high mill, the deformation model of the work roll was regarded as a cantilever beam and new influence coefficients were deduced. The effect of the bending force was taken into account independently. Therefore, the contribution to work roll deflection caused by rolling load, rolling pressure between rolls and bending force can be got from the new formulas. To validate the accuracy of the formulas, the results obtained from the new formulas were compared with those from SHOHET’s formulas. It is found that they highly coincide, which illustrates that the formulas are reliable. Key words: work roll; influence coefficient; cantilever beam; bending force
J. Cent. South Univ. Technol. (2010) 17: 1000−1005 DOI: 10.1007/s11771−010−0590−5
Improved model to solve influence coefficients of work roll deflection
2 Formulations derivation
Due to symmetry, the calculation process involves only one half of the roll system along the roll barrel. Fig.1 represents the slit beam model where jacks between the upper and lower work rolls as the bending mechanism are used, where Fb is the bending force for one chock; L4 is the length of work roll bearing central line; L5 is the length of work roll neck; db and dw are diameters of backup and work roll neck, respectively; Db and Dw are diameters of backup and work roll barrel, respectively; η and β are the distances from original to the jth and the ith elements, respectively; p(j) is the rolling pressure at the jth element; q(j) is the intermediate pressure between the backup roll and work roll at the jth element. The barrel lengths of the work roll and the backup roll are divided into n equilong elements and the strip is divided into m elements. The rolling pressures between the rolls and the rolling force are also discretized in the same manner. The pressure between work roll and backup roll, and that between the work roll and the strip are uniform in each element, which are replaced by a concentrated load applied to the middle of each element. The profiles of the deformed work roll and backup roll are obtained by calculating the roll deflection due to bending moments and shear forces. SHOHET’s calculation model is shown in Fig.2, where p1 represents the unit force and p2 represents the
ZHAO Tie-yong(赵铁勇)Engineering, Yanshan University, Qinhuangdao 066004, China © Central South University Press and Springer-Verlag Berlin Heidelberg 2010