Study On Bifurcation And Chaotic Behaviors Of Rolling Mill’s Main Drive Nonlinear Torsional Vibration System

Mill main drive system is an important part of rolling mill. In recent years, withrolling speed rises again and again, torsional vibration of mill main drive system isincreasingly prominent. Torsional vibration of rolling mill has an influence on quality andquantity of the products, even has a devastating damage on rolling equipments, sotorsional vibration of mill main drive system has important research value in modern steelindustry. This paper conducts systematic researches on nonlinear torsional vibrationsystem of rolling mill from three aspects, namely system modeling, stability analysis andcontrol method of torsional vibration system. By using analytical method, the unstableoscillation law and control strategy of torsional vibration system are given, whichpromotes mill vibration theory and application in further development.Firstly, considering the influence of nonlinear factors such as system structureparameters and outside disturbance incentive, the universal dynamics equation of millmain drive torsional vibration system with nonlinear stiffness and outside disturbance isestablished based on the generalized dissipative system Lagrange principle.A nonlineartime-delayed feedback controller is proposed. Under the condition of main resonance,perturbation analysis of the controlled system is carried out with the method of multiplescales. The influence of time delays on Hopf bifurcation and limit cycle is studied basedon Hopf bifurcation theory. The stability conditions and amplitude formula of limit cycleare given. Finally, numerical simulations are performed to verify the analytical results.Secondly, considering the influence of combination harmonic incentive, thebifurcation response equation of main drive system under combination resonance isdeduced with the method of multiple scales. Singularity analysis is employed to obtain thetransition set of steady motion. Melnikov function of heteroclinic orbit is solved accordingto heteroclinic orbit parameter equation of main drive system. The critical condition ofchaos about Smale commutation is given. Finally, numerical method is employed toanalyze the influences of different system parameters on chaotic motion by bifurcationdiagram, the maximum Lyapunov, phase trajectory and Poincare map.Thirdly, considering the influence of strong nonlinear stiffness, the dynamicalresponse of strong nonlinear torsional vibration system with two and three times nonlinear stiffness is solved with the method of MLP. Bifurcation characteristics of main drivesystem are analyzed in the autonomous and non-autonomous situations by means ofsingular point stability theory and singularity theory, respectively. Under main resonancecondition, the stability of bifurcation response equation is discussed, and the topologicalstructure of bifurcation curve is given. The bifurcation diagram of system responsecorresponding to the change of torsional rigidity is derived by using numerical simulations,and evolution process of period, period doubling and chaotic motions is studied. Finally,chaotic motion of main drive system can be controlled as stable period-2motion by directvariable feedback method.