| The membrane material in the printing industry can be molded into the axial motion of the membrane during the process of printing or processing.In the process of printing,the membrane will be affected by external factors,and unnecessary vibration will be generated in the process of printing.The speed and tension of the membrane will change with the change of coil diameter,and the surrounding airflow field will also change,which will cause membrane vibration intensification,and then affect the printing quality of finished products.The membrane vibration is intensified,which affects the overprinting accuracy of the printed matter.This paper considers the effect of air resistance and models the air resistance as a follower force,reference is made to the basic parameters of FR-400 gravure printing machine in northern shaanxi province,study the vibration characteristics of moving membrane under different working conditions and following forces.Finally,the active control of uniform and variable speed moving membrane vibration under the action of follower force is studied.The main research contents are:(1)The transverse vibration differential equation of the moving membrane under follower force is established by differential quadrature method.The vibration characteristics of the moving membrane under different boundary conditions are studied.The relationships of the first three dimensionless complex frequencies between the dimensionless speed,the tension ratio and the aspect ratio of the membrane are analyzed by numerical calculation.The vibration characteristics and stability of moving membrane under different conditions were analyzed.(2)The calculation model of moving membrane under different follower forces is established,and the differential equation of transverse vibration of axial moving membrane is obtained.The differential equation is used to discretize the transverse vibration equation of moving membrane,and the complex eigenvalue equation of moving membrane is obtained.Analyze the relationship between the dimensionless complex frequency and the dimensionless velocity under different follower forces of the moving membrane,and discuss the influence of the change of the follower force on the dynamic vibration characteristics and stability of the axial moving membrane.(3)The transverse vibration active control of moving membrane under the follower force based on the suboptimal control method in two boundary conditions is studied.By using the finite-difference method,the discrete vibration differential equation of the moving membrane with two kinds of movement form is obtained and the state equation of transverse vibration control system is derived.By numerical calculation,the curves of vibration response of the uniform and variable moving membrane are obtained.The results show that by means of suboptimal feedback control method,the transverse vibration of moving membrane in the two kinds of boundary conditions can be decreased rapidly and significantly close to stable state in a short time. |
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