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In this study, a probabilistic analysis of the critical velocity for an axially moving cracked elastic and isotropic plate is presented. Axially moving materials are commonly used in modelling of manufacturing processes, like paper making and plastic forming. In such systems, the most serious threats to runnability are instability and material fracture, and finding the critical value of velocity is essential for efficiency. In this paper, a formula for the critical velocity is derived under constraints for the probabilities of instability and fracture. The significance of randomness in different model parameters is investigated for parameter ranges typical of paper material and paper machines. The results suggest that the most significant factors are variations in the crack length and tension magnitude. [ABSTRACT FROM AUTHOR]

The model for the analysis of vibrations of paper in a printing device is presented. It is assumed that paper performs transverse vibrations as a membrane having stiffness due to static tension in its plane. The first eigenmodes are determined. It is shown that the eigenfrequencies of transverse vibrations of the analyzed paper can be controlled by the static tension in the plane of the paper. The model for the analysis of stability of paper in a printing device is presented. It is assumed that paper moves with constant velocity in a given direction. The analysis is performed using a plate-bending element with the contribution of the forces of inertia from the convective accelerations. This results in the eigenproblem determining the critical velocities and stability eigenmodes. The stand was made for obtaining the experimental investigations. Using it the nodal lines of the standing waves were determined and using projection moiré the eigenmodes were determined. The obtained results are used in the process of design of the elements of the printing device. [ABSTRACT FROM AUTHOR]