Bifurcation and chaos for piecewise nonlinear roll system of rolling mill

Abstract

A non-smooth cold roll system of rolling mill is studied to reveal the bifurcation of the piecewise-smooth and discontinuous system. To examine the influence of the parameters on the dynamics, the bifurcation diagram is constructed when it is unperturbed. Hamilton phase diagrams of the non-smooth system are detected, which differ significantly from the ones obtained in the smooth system. Non-smooth homoclinic, heteroclinic, and periodic orbits are determined, which depend on the classical heteroclinic periodic orbits, periodic orbits, and a necessary condition. A extended Melnikov function is employed to obtain the criteria for the non-smooth homoclinic bifurcation in this class of piecewise-smooth and discontinuous system, which implies that the existence of homoclinic bifurcation arises from the breaking of homoclinic orbits under the perturbation of damping. The results reveal that this kind of non-smooth factor has little influence on the chaotic threshold apart from calculating piecewise integrals. The efficiency of the criteria for non-smooth homoclinic bifurcation mentioned above is verified by the phase portraits, Poincaré section, and bifurcation diagrams, which laid a theoretical foundation for parameter design, stable operation, and fault diagnosis of rolling mills.