Nonlinear dynamics of rolling deformation zone: from singularity analysis to chaos threshold prediction

This paper focuses on the nonlinear dynamic behavior of the rolling deformation zone under complex operating conditions, where strong frictional nonlinearity, external excitation, and structural coupling may trigger severe instability and chaotic vibrations that are difficult to predict using conventional linear theories. To this end, a two-degree-of-freedom coupled mathematical model is established, which incorporates nonlinear stiffness, Stribeck friction, and periodic external excitation. Within this framework, the bifurcation, hysteresis, and chaotic evolution characteristics of the system are systematically explored. Based on singularity theory, the vector field ratio is introduced as the periodic perturbation parameter, whereby algebraic criteria for bifurcation and hysteresis sets are derived, which enables an explicit characterization of the parameter regions associated with stability loss and multi-solution coexistence. On this basis, the extended Melnikov method is further applied to investigate the splitting conditions of homoclinic and heteroclinic orbits under external excitation, and the critical threshold for the system to enter chaos is obtained. Moreover, theoretical derivations are corroborated by numerical simulations, which confirms the rationality and effectiveness of the proposed criteria. Overall, the research results not only reveal the intrinsic mechanisms underlying nonlinear behavior in the rolling deformation zone but also offer a unified analytical framework that combines singularity theory and Melnikov analysis for predicting global bifurcations and chaos in strongly nonlinear rolling systems, thereby providing new theoretical insights and practical guidance for stability assessment and vibration suppression in rolling processes.