Stability analysis of chatter in tandem rolling mills-part 2: The regenerative effect

Using the multi-stand chatter models derived in Part 1, a stability analysis, based on the integral criterion of stability for delay differential equations, will be carried out for the regenerative mechanism to better understand the effects of rolling parameters on regenerative instability. It will be shown that the interactions between consecutive stands through the time delay effect of the strip thickness variations consistently boost the tendency of each stand to chatter and, therefore, reduce the stability of the rolling process. Simulations will demonstrate stable and unstable behaviors of multi-stand rolling mills and aid in verifying stability charts created through stability analysis based on analytical models. They will be instrumental in identifying the critical vibration propagation paths of the regenerative mechanism in multi-stand mills through strip thickness and instant inter-stand tension variations. The critical vibration propagation paths of the regenerative mechanism will explain the modulation frequency observed in tandem mills that, as it will be shown, is inversely proportional to the shortest time delay during strip transport from the upstream stands to the downstream stands.