A nonlinear model describing the dynamical interaction between work rolls and metal sheets and the initiation of fifth octave rolling chatter is presented. The model, which comprises a work roll sub-model and a metal sheet roll-bite sub-model, enables the instability of strip rolling to be qualitatively and quantitatively studied as a function of rollstack stiffness, rolling speed, inter-stand tension, roll-bite entry and exit thickness, and the sheet force resulted from the interactive action of the work roll with the plastic deformation of the rolled strip. It is concluded that, even though the governing dynamics is highly nonlinear, rolling chatter instability is none other than mode excitation or beating, and thus linear. Analyzed results correspond well with what have been observed in physical rolling mills. Specifically, the natural frequency predicted for a 4-H rolling stand fits the fifth octave chatter at 550∼650 Hz and there is a critical rolling speed (2.54 m/sec for the material and sheet configurations considered in the paper) beyond which rolling instability will occur. This research establishes the fundamental knowledge base required for the understanding of chatter characteristics and mechanism, and thus provides the essential bases for effective control of rolling instability and chatter-free roll mill design.

We study the thermodynamic limit of very long walks on finite, connected, non-random graphs subject to possible random modifications and transportation capacity noise. As walks might represent the chains of interactions between system units, statistical mechanics of very long walks may be used to quantify the structural properties important for the dynamics of processes defined in networks. Networks open to random structural modifications are characterized by a Fermi–Dirac distribution of node’s fugacity in the framework of grand canonical ensemble of walks. The same distribution appears as the unique stationary solution of a discrete Fokker–Planck equation describing the time evolution of probability distribution of stochastic processes in networks. Nodes of inferior centrality are the most likely candidates for the future structural changes in the network.

System instability and chaotic response are the failure modes that could significantly impact the reliability and operating safety of high-speed rotor-dynamical machines. Initiation and propagation of surface cracks in rotary shafts are common causes for such failure modes. To be able to detect the onset and progression of these faults will considerably extend the lifetime and improve the reliability of the mechanical system. A wavelet-based algorithm effective in identifying mechanical chaotic response has been applied to determine the nonlinear dynamical characteristics of a model-based, cracked rotor. This investigation confirms reported correlation of surface crack breathing with rotor chaotic motions. The effectiveness of the algorithm in detecting rotor-dynamic instability induced by mechanical faults as contrast to algorithms that are based on nonlinear dynamics is discussed. The results show not just the feasibility of the algorithm in mechanical fault diagnosis but also suggest its applicability to in-line, real-time condition monitoring at both the system and component levels.

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