Nonlinear Dynamic Analysis of a Parametrically Excited Cold Rolling Mill

In this work, a four high cold rolling mill is modeled as a spring-mass-damper system considering horizontally and vertically applied time-dependent forces due to the interaction between the strip and the working rolls. The effect of vibration of the moving strip on the work roll vibration is also considered for developing the governing equation of motion of the system which is found to be that of a nonlinear parametrically excited system. The governing equation of motion is solved by using the method of multiple scales to find the instability regions and frequency-response curves of the system. The critical amplitude of horizontal load in roll bite is calculated and the frequency-response is studied in detail considering the effect of various process parameters, such as velocity, thickness of strip, time delay, amplitude, and frequency of horizontal load in roll bite. This work can find application in the design and development of high speed and chatter free rolling mills.