Study On Hopf Bifurcation Control And Codimension-2 Bifurcation Of Torsional Vibration Model For Main Drive Electromechanical Coupling System Of Rolling Mill

In industrial rolling mill equipment,whether the mill main drive electromechanical coupling system can maintain smooth operation,which is directly related to the quality of the rolled product and further affect the benefits of the related enterprises.The most important factors are the main drive system of the mill due to its instability oscillation and non-linear torsional vibration.Generally,the main drive system of the mill movement and dynamic behavior can be portrayed by differential equations,which requires us to study the mathematical model of such system at a deeper level.However,at present,the main drive system of the mill bifurcation control and mechanism research on high-codimension bifurcation and other topics still need to be discussed,there are still many shortcomings to overcome.Therefore,this thesis starts from the torsional vibration problem of the main drive electromechanical coupling system of the mill,and gives the conditions for the Hopf bifurcation and the codimension-2 bifurcation of the main drive system of the mill in detail by using the basic theory of generalized differential equations,and provides an effective method to achieve the bifurcation control.This is not only a refinement and development of the bifurcation theory of the existing mill main drive electromechanical coupling system,but will also provide some reference solutions for solving high-codimension bifurcation problems of nonlinear systems in other engineering.A series of issues such as stability,bifurcation control and high-codimension bifurcation analysis of such system are investigated in depth throughout the thesis,with the following main core work:(1)In order to suppress the instability of the electromechanically coupled mill main drive system,the thesis employs a non-linear feedback control technique to regulate the Hopf bifurcation of such system.Moreover,which will enhance the robustness of such system against disturbances.Specifically,by applying a non-linear feedback term to the mill main drive,it is possible not only to extend the region of steady-state operation of the system,but also to regulate the amplitude of the mill main drive’s vibration cycle.(2)To investigate the effect of the mill system components’ damping characteristics and the coupling strength on such system,this thesis establishes an electromechanical coupling system with fractional order mill main drive,reveals the stability law of the mill main drive system at the zero equilibrium point and non-zero equilibrium point respectively,and clarifies the mechanism of steady state control of the mill main drive system with fractional order as the main control parameter.In addition,a more general fractional order model is developed,which will also provides a new method to solve engineering problems.(3)To uncover the mechanism of the combined effect of feedback parameters and time delay on such system,in this thesis,we investigate the Bogdanov-Takens(codimensional-2)bifurcation of such system by using the feedback parameters and time delay as bifurcation parameters.The thesis rigorously demonstrates the analytical conditions for the Bogdanov-Takens bifurcation to occur and gives detailed phase diagrams and bifurcation diagrams corresponding to the universal opening and folding of the mill main drive system.Moreover,it is found that the codimensional-2 bifurcation of the mill main drive system is formed by the coupling of some typical codimensional-1bifurcations(Saddle-node bifurcation,Hopf bifurcation and Saddle homogeneous bifurcation),which has certain theoretical significance for the study of the mill main drive system torsional vibration problem.(4)To elucidate the relationship between the strong vibration behaviour of such system and its dynamical model cycle burst behaviour,the Hopf-Fold bifurcation of such system with time delay is analysed in this paper,drive shaft torsional stiffness and rotational inertia as the study parameters.The topological classification of the Hopf-Fold bifurcation at the critical point is also analysed with the aid of central manifold theory and the normal form method.In particular,the generated conditions under which the vibration outburst behaviour of the mill main drive system are given.