Study On The Dynamics And Vibration Control Of The Moving Paper Web

The study of the vibration and stability of the axially moving systems is of great significance. The main existing subjects are mainly about the axially moving beam, the axially moving column and the axially moving plate. Few papers have been presented on the moving paper web. In this paper, the moving paper web are the object of study. The tranverse vibration and stability of the moving paper web with elastically restrained edge, intermediate rigid support and intermediate elastically support are researched. The stability region of the accelerating paper web, the control of the moving rectangular paper web and the technique of vibration cutting for paper are analyzed respectively in this paper. The main research works are as follows.(1) The vibration problems of the moving rectangular paper web with the edge attached to distributed elastic restraint are studied. The element-free Galerkin method is proposed to solve the transverse vibration of the moving rectangular paper web with elastically restrained edge. Based on the extended Hamilton's principle for the elastic dynamics system, the dimensionless equations of motion of the moving rectangular paper web with elastically restrained edge are established by the element-free Galerkin method, and the eigenvalue equations are presented. Via numerical calculation, the curves of the vibration frequency of the moving rectangular paper web versus dimensionless moving speed and the elastic stiffness of edge elastically restrained are obtained. The effects of moving speed and edge elastically restrained on the free vibration characteristics of the moving rectangular paper web are analyzed as a conclusion.(2) The tranverse vibration and stability of the moving paper web with intermediate rigid support and intermediate elastically support are researched respectively. The Laplace transforms method is proposed to solve the transverse vibration of the moving rectangular paper web with intermediate rigid support and elastic support. According to D Alembert theory, the differential equation of motion and the eigenvalue equations of the moving rectangular paper web with intermediate rigid support and elastic support are obtained. The vibration frequencies on the condition of four edges clamped are obtained by the Laplace transforms method. The relationships of the first three order steps of vibration frequency versus velocity, tension, the stiffness of intermediate elastic support and intermediate support position of paper web are obtained.(3) The dynamics and stability of the moving rectangular paper web with linearly and half-sinusoid varying density are investigated. The dimensionless equation of motion of the moving rectangular paper web with varying density is obtained by introducing dimensionless variables and parameters. The complex eigen-equation is derived by the discretization of the dimensionless equation of vibration modes and boundary conditions using the Differential Quadrature method. The first three order steps of vibration frequency of the system is obtained by numerical calculation and the effects of the tension ratio, aspect ratio, the dimensionless moving speed and density coefficient on the dynamic behavior and stability of the moving rectangular paper web are analyzed.(4) The stability region of the accelerating paper web is developed when the speed is superposition by mean velocity and harmonic velocity. The influence on the stability region of the accelerating paper web exerted by the mean velocity, the amplitude of harmonic velocity, tension ratio of paper web and aspect ratio is investigated.(5) The transverse vibration control of the moving rectangle paper web with varying density is studied. The state equation of transverse vibration control system is obtained by using finite difference calculus to separate the dynamical equation. The suboptimum method is used to control the transverse vibration of the moving rectangle paper web. Then the response and the attenuation state of the transverse vibration of the paper web are presented by simulation analysis. It shows that suboptimum method can control the transverse vibration of the moving rectangle paper web effectively.(6) The use of vibration cutting technology in the printing machinery is studied. The new technology of vibration cutting in cutter is realized. The cutting resisting force of cutting bed and the severe shock of cutter beared are reduced significantly. The test-bed of vibration cutting is designed, and the vibration test system is built. The optimum excited frequency has been obtaind on the basis of theoretical calculation and experiments.