Parametric oscillations of single-cell reversible cold rolling mills

One of the reasons for the appearance of self-oscillations in cold rolling mills is the nonconservative hydrodynamic forces acting on the working rolls during the rolling process. In the thin gaps between the working roller and the steel strip, a hydrodynamic wedge appears. In the case of an asymmetric gap and a sufficiently high rolling speed, nonconservative forces arise in the wedge, leading to self-oscillations. The pattern of self-oscillations is similar to the occurrence of self-oscillations in open sliding bearings. In multicellular cold rolling mills and two-cell reversible mills, the amount of tension between the crates has a significant effect on the process of self-oscillation. Therefore, the simplest and most logical model can be two oscillators described by the Van der Pol equation connected by an elastic band. This model allows not only to investigate the effects of synchronization and frequency capture under external influence, but also to take into account the effect of tension on the process of self-oscillation. In single-cell reversible mills, there is only one oscillator in which self-oscillations can originate, and this is the working cage. On a single-cell mill, the rental is carried out in several passes. At each pass, a winder is used as the second crate, which should form the tension of the rolled strip. In the case of single-pass rolling, the tension of the strip in the mill cage is created directly on the uncoiler, which lacks the conditions for the formation of non-conservative hydrodynamic forces. If a filling roller is installed on the uncoiler and the roller can be represented as a console or a pendulum, then the uncoiler can be considered as a parametric oscillatory system. In this case, two oscillators connected by an elastic band can be considered as a model of a single-cell rolling mill. The rolling cage is described by the Van der Pol equation, the uncoiler is described by the Mathieu equation. This model allows us to study the influence of parametric vibrations of the decoiler, self-oscillations of the working stand of the mill and the influence of the tension of the rolled strip on the process of synchronization and frequency capture. As a result of the simulation, dependences on the amount of damping and the level of the Mathieu parameter for even and odd ultra harmonics of mill harmonics are obtained. The first and second harmonics make harmonic or quasi-harmonic vibrations, the third and subsequent harmonics make complex inharmonic vibrations.