Global Dynamic Analysis And Control Research On Vertical Vibration Of Rolling Mill System

The rolling mill system is widely used in steel rolling equipment.Due to the influence of many nonlinear factors in the system,it exhibits complex nonlinear vibration characteristics.These vibration characteristics seriously affect the working performance and reliability of the system,restrict the stability,compactness and efficiency of the rolling production process,and seriously affect the development of iron and steel industry.Therefore,the research on the dynamic characteristics of the rolling mill system has important theoretical and engineering significance.Firstly,considering the factors of rolling mill gap and nonlinear stiffness,a kind of kinematic differential equation of vertical vibration of rolling mill system is established.The variable step Runge-Kutta method is used to solve the differential equation of the system.The bifurcation diagram,phase diagram and Lyapunov exponent diagram are obtained to analyze the motion evolution law of the system.Using the incremental harmonic balance method,the approximate analytical solution of the periodic motion of the system under the external periodic excitation is calculated,and its phase diagram is drawn.The stability of the periodic solution of the system is determined by Floquet multiplier,and compared with the solution of Runge Kutta method,the path from periodic doubling to chaos is analyzed.Secondly,the global dynamic characteristics of the system are studied by numerical methods,the bifurcation and chaos characteristics of the main parameters of the system are studied by combining single parameter bifurcation diagram,dual-parameter bifurcation diagram,phase trajectory diagram,Poincaré map and Lyapunov exponent spectrum.Based on the cell mapping method,the attractor and the attraction domain of the system are obtained,and the multi-stable dynamics and evolution law of the system are studied.Combined with the multi-initial value bifurcation diagram,various multistable dynamic characteristics of the system in the specific parameter interval are analyzed,including the coexistence of multiperiod attractors and the co-existence of periodic attractors and chaotic attractors.Then,since chaotic motion is generally not expected in practical engineering,in order to avoid high-energy-consuming periodic motion and chaotic motion in various steady states with specific parameters,the multistable control under the condition of changing excitation frequency and external excitation amplitude is studied,a linear augmentation scheme is used to control the system motion to an orbit with lower energy consumption.Finally,considering the vertical vibration of rolling mill system under quasi-periodic excitation,its singular and non-chaotic dynamic characteristics are studied.The singular properties of the attractor are verified by means of phase-sensitive function and rational number approximation to irrational number,and its non-chaotic properties are characterized by numerical methods such as Lyapunov exponent spectrum and phase diagram.It is found through numerical methods that three routes can evolve into strange nonchaotic attractors,namely fractal route,intermittency route and Heagy-Hammel route.