Due to several physical causes, high-amplitude, undesirable mechanical vibrations, called chatter, can be experienced during hot and cold rolling processes. To study this instability phenomenon, several authors have distinguished third octave and fifth octave chatter based on the vibration frequency. While fifth octave chatter mainly causes quality issues on the products, third octave chatter is much more problematic. This vibration can provoke strip break and, therefore, cause severe damage to the mill. Previous studies have shown that third octave chatter is linked to a regeneration effect due to stand coupling. It has also been demonstrated that there exists a critical speed above which the vibration becomes unstable. Therefore, the main actuator used to control third octave chatter is a speed reduction, resulting in a loss of productivity.
In the presented work, a numerical model was designed to study third octave chatter with low computational costs. The model was developed using MATLAB/Simulink, and each stand is represented by mass-spring-damper systems, which link the different elements of the stand. The mechanical behavior of the strip in the roll bite is non-linear and generally requires a more complex model. In the proposed model, this behavior is linearized around the working point. Additionally, consecutive stands are coupled by variations in the strip tension and thickness transportation.
The proposed model was utilized to calculate the stability of various operating points. It is possible to compute the critical speed for each set of parameters, which includes working points, reduction, mass, stiffness, damping of various elements, and friction coefficients. Sensitivity studies were conducted to determine the impact of each parameter on the critical speed. In the second step, the model can be employed to evaluate different actuators with the aim of controlling third octave chatter.
