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. T...
Highlights
Due to the non-smooth characteristic, the research was not focused on the global bifurcation of the piecewise nonlinear dynamic model of rolling mill
The results reveal that this kind of nonsmooth factor has little influence on the chaotic threshold apart from calculating piecewise integrals for this class of nonlinear dynamical system (17)
The results presented above show that the vibrations of the non-smooth roll system of rolling mill have rich dynamic behaviors depending on f, which may lead to the potential hazard
Summary
With the development of science and technology, the investigations on vibration and control of a nonsmooth system have been of great significance inengineering.[1,2,3] Melnikov’s method, a tool to obtain analytical results, has been extended to piecewise-smooth dynamical systems by geometrical or analytical technique.[4,5,6,7,8,9,10,11,12,13,14] It is important to note that the particular piecewise-smooth dynamical system was investigated in Tian et al.[11,12,13] and Niziol and Swiatoniowski.[14]. Keywords Piecewise nonlinear system, rolling mill, non-smooth homoclinic orbit, bifurcation, chaos Due to the non-smooth characteristic, the research was not focused on the global bifurcation of the piecewise nonlinear dynamic model of rolling mill.
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