Self-oscillation of single-cell reversible cold rolling mills under periodic external force

During cold rolling of thin strips, self-oscillations occur under certain conditions. The cause of self-oscillation is the nonlinearity of the rolling process, the occurrence of negative damping in the contact zone, synchronization and frequency capture in the last stands of multicellular mills, and instability of the rolled band at high rolling speeds. Modeling the self-oscillation process is a complex process, using both experimental and numerical methods. The rolling process control system can also have a significant impact on the process of occurrence and passage of self-oscillations. During the operation of single-cell reversing mills, the dependence of the self-oscillation frequency on the rotation frequency of the working rolls was experimentally obtained. Moreover, the occurrence of self-oscillations occurs with frequency capture as an ultraharmonic oscillation. In addition, during the operation of the automated process control system, control signals are generated for the rolling force with a frequency of self-oscillations. Thus, the working rolls form ultraharmonic vibrations, AS well as harmonic frequency capture. The mill is regulated by PI and PID regulators, which are essentially linear systems. As long as the mill retains the properties of a linear oscillatory system, the mill operates normally. With the advent of self-oscillation, the mill becomes a significantly nonlinear system and problems may arise in the control of the mill. Using the Van der Pol equation, a numerical analysis of the mill's behavior under the influence of external forces generated by working rolls and automated process control systems was carried out. It is shown that a nonlinear self-oscillating system remains at rest under zero initial conditions and the absence of external forces. When an external influence is applied to the system with a frequency far from the frequency of self-oscillations, forced oscillations occur in the system, and an auto-oscillatory mode is formed. In this case, ultraharmonic vibrations can be formed. When the system is affected by forces with a frequency equal to the frequency of self-oscillations, harmonic frequency capture is formed. The formation of conditions for the occurrence of self-oscillations of a single-cell mill can be carried out directly by the mill cage and additionally enhanced by the impact of automated process control systems.