Dynamic Modeling and Vibration Analysis in Cold Rolling Systems

Cold rolling systems convert metal slabs into sheets through deformation between rotating rolls. Throughout this process, dynamic interactions between the rolling workpiece, roll stands and control systems give rise to complex vibration phenomena. Accurate dynamic modelling is essential for predicting and mitigating chatter, a self-excited oscillation that degrades strip quality and may damage mill components. Traditional models treat the mill as a lumped mass–spring–damper system coupled to rolling force formulations that account for strip deformation. More advanced formulations incorporate multiple degrees of freedom, capturing vertical, horizontal and torsional modes and their nonlinear coupling. These models enable stability maps for process parameters, guiding the selection of rolling speed, tension and lubrication to avoid resonance. Nonlinear analysis techniques, including bifurcation theory and power flow methods, reveal how changes in stiffness, damping and excitation forces can trigger abrupt amplitude changes or chaotic responses. Recent advances integrate particle or active damping technologies, hydraulic control dynamics and data-driven approaches to enhance predictive accuracy and to design adaptive vibration suppression strategies. The global importance of this research lies in its impact on energy efficiency, product consistency and the extension of mill service life.

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Recent studies have introduced a particle damping dynamic vibration absorber to control vertical roll oscillations by converting vibrational energy into heat. A nonlinear model of the absorber–roll system was developed and solved via harmonic balance, while power flow analysis guided the selection of absorber parameters. Experimental tests on a pilot mill confirmed substantial amplitude reduction, emphasising the potential for retrofit damping solutions.

In parallel, machine learning techniques have been applied to forecast strip mill vibrations. An extreme gradient boosting model was trained on operational data and fine-tuned using Bayesian optimisation, yielding superior prediction accuracy and computational efficiency. Model interpretability was enhanced with SHAP values, revealing the relative influence of process variables on chatter risk.

Foundational work on tandem cold rolling mills has focused on multimodal coupling of vertical, horizontal and torsional vibrations. A nonlinear dynamic model incorporating rolling force interactions demonstrated the onset of self-excited chatter through Hopf bifurcation. Stability charts derived from this model inform the design of rolling schedules that avoid unstable operating regimes.

Dynamic Modeling and Vibration Analysis in Cold Rolling Systems publication trend

The graph below shows the total number of articles in dynamic modeling and vibration analysis in cold rolling systems across all publications each year (not limited to Nature Index journals).

Technical terms

Chatter: self-excited vibration of rolling mill rolls driven by regenerative feedback between successive passes, leading to surface defects.

Bifurcation: change in the qualitative behaviour of a nonlinear dynamic system when a control parameter crosses a critical threshold, often leading to oscillations or chaos.

Dynamic rolling force: time-varying contact force between work roll and strip, influenced by strip deformation and mill dynamics.

Vibration absorber: device, passive or active, designed to reduce oscillations by dissipating or redirecting vibrational energy.

Harmonic balance method: analytical technique for approximating periodic solutions of nonlinear differential equations by balancing harmonic components.

References

1. Transmission and Dissipation of Vibration in a Dynamic Vibration Absorber-Roller System Based on Particle Damping Technology. Chinese Journal of Mechanical Engineering (2024).
2. Vibration prediction and analysis of strip rolling mill based on XGBoost and Bayesian optimization. Complex & Intelligent Systems (2022).
3. Stability Analysis of a Nonlinear Coupled Vibration Model in a Tandem Cold Rolling Mill. Shock and Vibration (2019).