Study On The Dynamic Behavior Of The Piecewise Nonlinear Dystem Of Rolling Mill

Rolling mill is the key part of the iron industry and also is the core equipment of rolling industry. In recent years, modern industry is rapidly developed and the demand for the specifications of steel products becomes more stringent. However, as the nonlinear factors increase in the rolling process, the vibration of the rolling mill affects the accuracy of products, which becomes one of the key factors. Hence, researchers pay close attention to the research on vibration of rolling mill. This paper is based on the simplified model of vertical vibration model of rollers. By using the extended classical Melnikov method and the basic theory of nonlinear dynamics, the vibration of rolling mill is carried on the qualitative and quantitative analysis and calculation. And the correctness of theory is verified by numerical simulation. The main contents of the paper is arranged as follows:In Chapter 1, we simply introduce the research background and the current situation of nonlinear dynamics. Main research contents and main innovative points in this paper are briefly summarized.In Chapter 2, the simplified model of vertical vibration model of rolling mill is briefly introduced. We obtain the piecewise dynamic equation of the vertical vibration based on the dimensionless method. We discuss the equilibrium distribution when the piecewise system is unperturbed by considering the mode of vertical vibration. A type of non-smooth heteroclinic orbit, homoclinic orbit and periodic orbit is determined which depends on the classical theory of orbit and different types of equilibrium. And the Hamilton phase diagrams of the piecewise-nonlinear system are simulated using Matlab and Mathematica.In Chapter 3, a type of non-smooth heteroclinic orbit, homoclinic orbit and periodic orbit are presented analytically, based on the classical heteroclinic orbit, homoclinic orbit and periodic orbit.In Chapter 4, a new extended Melnikov method is employed to obtain the criteria for chaotic motion, which implies that the existence of heteroclinic orbits and homoclinic orbit to chaos rises from the breaking of heteroclinic orbits and homoclinic orbit under the perturbation of damping and external force. The efficiency of the criteria for chaos mentioned above is verified by bifurcation diagrams, the phase portrait and Poincaré surface of section. It is noting that the damping coefficient can impel it to the rich dynamics, such as periodic motion, quasi periodic motion and chaotic motion. In addition, we also discuss the hopf bifurcation of the system.In Chapter 5, we summarize the main results obtained in this paper and discuss the prospect of the model of vertical vibration.