Nonlinear Vibration And Stability Of Printing Membranes On Oblique Supports

The membranes are applied in many fields like military research,engineering science,mechanical equipment,aerospace,and the higher printing precision requirements are needed for preparing membrane products.In the process of membrane production,the oblique supports are one of the important parts of the printing equipment for the stable transmission of printing materials.The vibration characteristics of the printing membrane supported by the oblique roller are easily affected by the angle of the oblique supports.Continuous printing membrane in motion will appear intermittent tension fluctuation and harmful vibration.In this paper,considering the effect of the oblique supports,the oblique coordinate system is selected as the reference coordinate,and the basic parameters of B624 web press in Shaanxi Beiren are taken as the reference to study the nonlinear vibration characteristics of the moving membrane on oblique supports.(1)The vibration characteristics of printing membrane with oblique supports under multiple working conditions are studied.Based on D’Alembert principle,the mechanical model and differential equation of printing membrane are established.The impact of oblique support angle,aspect ratio and tension ratio on the stability of the system is analyzed by differential quadrature method.The key factors affecting the stability of the membrane on oblique supports are expounded,and the critical speed of stable transmission of the membrane is obtained.(2)The large deflection vibration characteristics of printing membrane on oblique supports under multiple working conditions are studied.Based on D’Alembert principle and von Karman large deflection theory,the mechanical model of moving membrane on oblique supports under multiple working conditions are established.The nonlinear free vibration characteristics of printing membrane on oblique supports are studied by using elliptic integral method.The impact of angle,initial parameters,velocity and aspect ratio of oblique supports on the dynamic of the system are analyzed,and the parameter range of stable transmission is obtained.(3)The nonlinear forced vibration characteristics of the moving membrane on oblique supports are studied.The mechanical model and nonlinear forced vibration equation of the membrane on oblique support under periodic excitation are established.The numerical analyses are conducted by using the fourth-order Runge Kutta method.The representation diagrams of nonlinear systems such as the bifurcation plots and largest Lyapunov exponent are obtained.The impact of the angle of the oblique supports,the amplitude of the external excitation,and the aspect ratio on the dynamic characteristics of the system are analyzed,and the parameter range of the stable transmission is obtained.