Vertical vibration model for the roll system of a six-high rolling mill based on the Timoshenko beam theory

During the production of cold-rolled strips, the high-speed operation of rolling mills generates vibrations that significantly impact the production efficiency, the strip quality, and the rolling mill service life. Therefore, investigating the vibration characteristics of rolling mills is of paramount importance. Previous studies predominantly treated the rolls as point masses, overlooking variations in the vibrations along the lengths of the rolls. In this study, the working, intermediate, and backup rolls were regarded as continuous elastic bodies, and they were simplified as Timoshenko beams. The modal superposition method was used to solve the vertical vibration equations for the rolls of a six-high rolling mill; thus, the natural frequencies and modal shapes for the rolls were obtained for both free and forced vibrations. A finite-element model validation confirmed that the accuracy of the novel Timoshenko beam six-high rolling mill vibration model introduced in this paper is significantly higher than that of the traditional Euler beam model when the roller length-to-diameter ratio is relatively small. Further analysis based on this model indicates that the forced vibration of the rolls is primarily influenced by fluctuations in rolling force. The amplitude of forced vibration is affected by factors such as the friction coefficient in the deformation zone, rolling speed, and cumulative rolling distance of the work rolls. These findings provide a precise representation of the characteristics of forced vibrations in rolling mills and offer valuable theoretical insight to ensure stable rolling mill operation.