Study on friction characteristics at the rolling interface under vertical-horizontal coupled vibration of rolling mill systems based on dynamic rolling force

This study addresses the limitations of conventional steady-state rolling models in characterizing metal flow dynamics and force-energy parameters at the rolling interface under vertical-horizontal coupled roll vibrations. Based on the principle of mass conservation, a three-dimensional velocity field for the strip was established. A dynamic rolling model of the rolling mill system was constructed by systematically analyzing the effects of coupled roll vibrations on micro-element deformation. An improved Tselikov-based rolling force calculation method was developed using a chord-to-arc approach for individual strip micro-elements to determine the evolution of the friction coefficient and the stress distribution during rolling. The results show that the rate of change in roll-gap height is linearly related to the horizontal roll vibration velocity, while increasing rolling speed reduces the friction coefficient and shifts the neutral point. For low-speed rolling of aluminum, the maximum relative error between the model-predicted rolling force and the measured value is 11.92%, and the average relative error is lower than that obtained with existing constant-friction coefficient models. The remaining discrepancy is mainly attributed to dynamic effects that are not fully captured during the rolling process. These results support the effectiveness of the model within the investigated operating range. The analysis further shows that vertical-horizontal coupled roll vibrations significantly influence the distribution of force-energy parameters at the rolling interface by dynamically modulating the contact arc length. The proposed framework provides a theoretical basis for optimizing rolling-process parameters through active control of roll vibrations and contributes to the development of vibration aware rolling technology.