Vertical vibration characteristics of cold rolling mill roll system under dynamic rolling force based on fractal theory

Vertical vibration of the mill roll system seriously affects the forming quality of the plate, and the rolling force is the main reason affecting the vibration of the mill; the accuracy of the rolling force model is crucial for rolling production. Fractal theory has garnered considerable attention owing to its self-similarity and multi-scale characteristics. Therefore, the vertical vibration model of a rolling mill under dynamic rolling force, considering fractal theory, is expected to achieve effective vibration suppression. In this work, considering the rolling interface contour fractal characteristics and the mutual coupling influence of solid contact force and emulsion contact force, a dynamic rolling force model with oil film thickness, contact area and rolling speed was established. Considering the mechanical structure of the plate and strip mill, a nonlinear vertical vibration dynamics model of the mill under dynamic rolling force was established. The vibration model was solved by the multi-scale method, and the main co-oscillation amplitude–frequency equations of the system were obtained. The effects of the main parameters on the vertical vibration of the rolling mill system, as well as the bifurcation characteristics, were studied. Simulations are performed using actual parameters and the results are shown: the dynamic rolling force primary term stiffness decreases, and the main resonance amplitude of the system increases and exhibits jumps; when the cubic term stiffness increases, the system exhibits jumps, and when the cubic term stiffness is zero, the system solution becomes stable and unique, with no jumps; the damping coefficient of the system increases and the vibration amplitude decreases; reasonable control of the external disturbance force can effectively improve the stability of the rolling mill system. The results of the study provide theoretical references for further suppression of vertical vibration in rolling mills.