Parameter Vibration and Dynamic Stability of the Printing Paper Web with Variable Speed

Abstract

Parametric vibration and dynamic stability of the printing paper web with variable speed were studied. The speed of the moving paper web was regarded as the sum of the constant mean speed and the sine pulse speed. The dynamical model and the transverse vibration differential equation were established. The period coefficient state equation was obtained by discretizing the space variable of the differential equation with the differential quadrature method and imported state vector. The instability region and the stability region of the paper web were determined by the implicit Runge-Kutta method. The relationships of the instability region versus the tension ratio, length-width ratio and the amplitude of the sine pulse speed were analyzed. The results provide a theoretical basis for optimizing the structure of the printing machine and improving the working stability of the paper web.Key words: the moving paper web with variable speed; parameter vibration; differential quadrature method; stability INTRODUCTIONThe printing speed and the production efficiency of web fed printing and gravure presses is becoming faster and higher. It is now being used in volume-production of newspapers, books and packing materials. The transverse vibration along the vertical direction of the tensioned paper web is caused by the eccentricity of the scroll in the printing process. The transverse vibration could affect the paper web's working stability, and thus influence the product quality seriously in paper-making, printing and the packing industry, Furthermore, the improvement of the working speed is restricted. So research into the transverse vibration and stability of moving paper web or membrane is of great important application value, and numerous workers have paid close attention to it.In 2002, Wu [1] studied axisymmetric transversal intrinsic vibrations of annular membranes of varying density with an amended perturbation method and obtained the characteristic equations which determine the transversal intrinsic vibration frequencies. In 2004, Wu [2][3] presented the characteristic equations of transverse intrinsic vibrations of membranes without axial movement in rigid middle supports. The transverse vibration and stability of axial moving membrane were studied by Hou [4]. He focused on the dynamic properties and stability of the membrane at constant speed vs. the length-width ratio and the tension ratio on the border of a rectangular membrane. In 2006, Shina [5] studied the dynamic characteristics of a homogeneous membrane with constant moving speed and obtained the differential equations by using an extended Hamilton principle. In the same year, Marynowski [6] built the elastic and viscoelastic model of viscoelastic cylinder material with axial movement speed by using the 2D-rheology theory. Giannoccaro [7] established a tension control simulation system of the web-fed press and performed simulation experiments. A new shell element has been proposed for geometrically

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