Study On Stability Of Periodic Solutions And Time Delay Feedback Control Of Rolling Mill’s Main Drive System

Torsional vibration is one of the main causes of damage of the rolling mill equipment. In a slight degree it would affect the quality of steel strip and decrease the fatigue life of transmission parts, or it may threaten the safety production of the whole transmission system and even lead to security incidents. So it is actually significant to research on the torsional vibration of the main drive of rolling mills.Focusing on the main drive of rolling mills, the article studies the nonlinear torsional vibration system of rolling mill from three aspects: system modeling, stability analysis and control method of torsional vibration system. The nonlinear vibration characteristics are studied by the incremental harmonic balance(IHB) method. Then periodic solutions of system are judged by using the Floquet theory and the impact of amplitude changes of the excitation on dynamic bifurcation characteristic of the system is obtained. At last, the paper analyzes control of the chaotic motions of the system by delayed feedback parametric through the numerical simulation method.Firstly, considering the influence of nonlinear factors such as gap and excitation, the general dynamic equation of the nonlinear torsional vibration system of rolling mill with nonlinear stiffness and excitation is established based on Lagrange principle of singular dissipative system. Then it provides the theoretical model for dynamic analyses and control of chaotic motion of the system.Secondly, the periodic solutions of the nonlinear torsional vibration system are obtained by the IHB method. It constantly carries out the process of increment and harmonic balance by taking excitation as the active increment. The IHB method is a semi analytic numerical method which can not only analyze in a qualitative way but also give quantitative results. The IHB method with three harmonics can achieve high calculation precision when compared with the fourth order Runge-Kutta method. The paper analyzes the impact on the dynamic bifurcation characteristic caused by changes of excitation. With the increase of excitation amplitude, the period doubling bifurcation route leading to chaos is observed. At last, the stability of the periodic solutions of system is judged by using the Floquet theory.Thirdly, the paper adds time delay to the main transmission system. The multiple scale method(MSM) is used to solve the nonlinear equations and the averaged equation and the frequency-response bifurcation equation are obtained. So the paper can reach the conclusion that the dynamic behavior of the system can be controlled by changing the delay parameters. At last, the control of the chaotic motion of system by the time-delay parameters is studied via numerical simulation.