Study on the transverse hardness distribution in strip-induced vibration of the Stand S4 cold rolling mill

Abstract To identify the root cause of the abnormal 186Hz vibration amplitude in Stand S4 of a cold rolling mill, this study analyzes the statistical characteristics of two distinct transverse hardness profiles across the strip width. The influence of both individual hardness distributions and their interaction with strip surface morphology on the amplitude frequency response of the Stand S4 is systematically investigated. A novel finite element simulation model is proposed to represent the spatially varying hardness distribution across the strip width, overcoming the limitations of conventional models that assume uniform or single-value hardness. The results demonstrate that the transverse hardness profile is a primary contributor to the excessive vibration at 186Hz. While surface morphology can amplify the vibration amplitude, the degree of amplification is modulated by the underlying hardness statistics. Specifically, the vibration amplitude exhibits a negative correlation with the mean hardness and a positive correlation with the standard deviation of hardness, highlighting the critical role of both average material properties and local non-uniformity in dynamic excitation.