Development of a Mathematical Model for the Prediction of Vibration in a Cold Rolling Mill Including the Driving System

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To date, a variety of analytical and mathematical dynamic models of a rolling mill have been developed, but they were simplified models involving the vertical vibration of the rolls and were not enough to be compatible with actual chatter vibration. In this paper, a mathematical model of a cold rolling mill including the driving system is proposed. The model is reliable enough to be compatible with experimental and theoretical analysis. It took into account the frictional forces between the rolls and the stiffness caused by the roller bearings and the contact between rolls. The joint forces of the spindle were computed from the force equilibrium equations in which the contact stiffness between the gears was approximated in a Fourier series form. To solve the model efficiently, a novel combination of the direct integration method and quasistatic analysis was proposed. The principal frequencies, including the gear mesh and chatter frequencies, predicted by the model were very similar to that determined by experimental and theoretical analysis. Not only the vertical, but also the horizontal vibration was investigated to study the added effect of the horizontal rolling force, frictional forces, and joint forces. The horizontal chatter vibration had a strong effect on the dynamic characteristics, although the chatter frequency was generated both in the vertical and horizontal directions.