Study On Nonlinear Vertical Vibration And Stability Control Of The Corrugated Rolling Mill Based On Dynamic Rolling Force

In traditional composite plate rolling technology,flat rolls are usually chosen as work roll to realize the composite of two kinds of metals.However,flat rolls easily causes large curvature warp and cannot realize continuous production in the actual production as the two kinds of metal have different rates of elongation.The composite sheet corrugated roll forming technology has broken through the bottleneck problems of traditional preparation technology,such as low strength,high residual stress and poor plate shape.It is a revolutionary and innovative technology with great development prospect,and provides a new idea for the preparation of high bonding strength and good plate shape metal layered composite plate.The corrugated rolling mill has the characteristics of multivariable,strongly coupled,non-linear,multi-constrained and time-varying.The roll shape curve of corrugated roller is usually cosine curve.During the rolling process of composite plate,the dynamic rolling force,the nonlinear damping and the nonlinear stiffness between corrugated roll and flat roll may cause complex dynamic behaviors,which presents a new challenge to the vibration research of rolling mills.In this paper,the nonlinear vertical vibration behavior and stability control of corrugated roll mill based on dynamic rolling force are studied.Firstly,through the combination of finite element software ABAQUS simulation and experimental testing,the change of rolling force during corrugated roll rolling and flat roll rolling is studied.The three-dimensional models of the 150 mm flat rolling mill and the 150 mm corrugated rolling mill are established through Solidworks software.The virtual prototype model of the flat roll mill and the corrugated roll mill is established in the mechanical dynamics analysis software ADAMS/View.The difference of dynamic rolling force and vibration characteristics between corrugated rolling mill and flat rolling mill is analyzed.Secondly,considering the dynamic rolling force,the nonlinear damping and nonlinear stiffness within corrugated interface of corrugated rolling mill,the two-freedom-degree mathematical model of nonlinear vertical vibration of corrugated rolling mill based on dynamic rolling force is established.The approximate analytical solution and amplitude-frequency characteristic equations of principal resonance and sub-resonance of roller system excited by dynamic rolling force are carried out by using the multiple-scale method.The influences of nonlinear stiffness coefficient,nonlinear damping coefficient,system damping coefficient and dynamic rolling force amplitude on principal resonance and sub-resonance are analyzed.The time-delay feedback controller with linear and nonlinear interactions is designed to control the principal resonance and sub-resonance of the corrugated roll system,and the correctness and feasibility of the controller are verified by numerical simulation.Thirdly,the singular value theory and the average method are used to discuss the stability of the corrugated roll mill under autonomous and non-autonomous systems.The transition sets,bifurcation curve and instability zone of the nonlinear vertical vibration system of corrugated rolling mill are analyzed by the singular theory and universal unfolding theory.The nonlinear parameter controller is designed to change the steady-state response of the nonlinear vertical vibration of corrugated rolling mill,reduce the corresponding amplitude of the system and eliminate the saddle-node bifurcation at resonance.The Lyapunov exponent,phase trajectory,Poincaré map and other chaotic motion numerical recognition features are used to analyze and verify the dynamic characteristics of the non-linear vertical vibration system of the corrugated rolling mill.The chaotic behavior of the system is effectively controlled by variable feedback dynamic bifurcation control and adjusting excitation amplitude dynamic bifurcation control.Then,this paper investigates Neimark-Sacker(N-S)bifurcations of corrugated rolling mill at resonance and the control of quasi-periodic vibration.The Poincaré map of system is developed by solving the power series solution of differential equation near equilibrium.Based on the Poincaré map,the existence of N-S bifurcation and the stability of quasi-periodic vibration in the case of 1: 3 and 1: 4 strong resonance and 1:5 weak resonance are analyzed.A nonlinear feedback controller is designed for 1:4 strong resonance N-S bifurcation.The governing equations of stability and amplitude of the trajectory section on the torus of quasiperiodic oscillation are analytically derived based on normal form approach.The control of quasi-periodic oscillation at 1:4 resonance is finally realized.In the end,based on the modern testing technology,the vibration testing system of corrugate rolling mill is established,and roll vibration characteristic test experiment in the process of preparing Cu/Al composite plate by corrugated rolling and flat rolling is carried out with 150 mm mill as the research object.The correctness of the virtual prototype and mathematical model is verified by comparing experimental results with numerical simulations.According to the nonlinear vertical vibration characteristics of the corrugated rolling mill and combined with theoretical analysis,a dynamic vibration absorber is designed.The amplitudefrequency characteristic curve equation of the dynamic vibration absorber installed in the system is solved by using the multi-scale method.The control effect of dynamic vibration absorber on nonlinear vertical vibration is studied by numerical simulation.The correctness and feasibility of the dynamic vibration absorber are verified.The research will make up for the deficiency of theoretical research on the dynamic characteristic analysis and stability control theory of the nonlinear vertical vibration system of corrugated rolling mill and provide important reference value and theoretical basis for the design and analysis of corrugated rolling mill.