Nonlinear Resonance Response and Stability Analysis of the Mill Vertical System


The vertical vibration universally exists in the running process of cold tandem mill system. Due to the rollers chatter, either the bright and dark stripes or the visible thickness difference can come into existence, which will seriously affect the quality and accuracy of products. For studying the characteristics and mechanism of vertical vibration, a lumped- mass model is established, in which nonlinear damper between top and bottom working roller are considered, and the rollers are connected with mill housing by nonlinear spring components. By means of the multiple-scales approach, the first-order analytical approximations of steady-state periodic solutions describing the primary resonance, super-harmonic resonance and sub-harmonic resonance are individually investigated. Through graphically depicting the amplitude- frequency response equations, the jump phenomena caused by nonlinear parameters are analyzed and numerically simulated. In addition, on the basis of the corresponding autonomous system, the stability of equilibrium solutions and self-excited periodic vibration is studied by using the Lyapunov stability theorem, and verified through numerical simulation of time- history and phase-plane trajectory. These research results are significant to reveal the mechanism of chatter, optimize the technology condition and improve the product quality in practical rolling process.

  • Abstract
  • Keywords:
  • Introduction
  • Nonlinear Dynamics Model
  • Resonance Response
  • Stability Analysis of Autonomous System
  • Conclusions
  • Acknowledgments
  • References

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