On the web tension dynamics in an open draw

Abstract

Increasing productivity of paper machines, i.e. speeds, and requirements on decreasing basis weights of paper grades demand a deeper insight of the web tension behavior in the open draws. Runnability of a paper machine is often determined by the web's sensitivity to breaks in the press and dryer sections, where the wet paper web has not yet reached its full strength. Often the measurement of variations in web tension is possible, but determining the factors causing these tension changes is difficult Mathematical models offer an efficient way to study qualitatively time-dependent physical phenomena in the web.

The aim of this paper is to study web dynamics in an open draw with the help of an advanced mathematical model by including flexural rigidity of the web and geometrically having rolls at both ends of the open draw. The model is based on two-dimensional finite element method (FEM), and both longitudinal and transverse forces have time-dependence in the open draw. FEM implementation of the model makes it possible to study phenomena of the moving web in a detailed manner. Different portions of the total forces affecting the web (inertial and external forces) can be calculated at desired points of the web. As a result, we obtain temporal tension distribution and web deflections. The FEM method offers versatile possibilities to study the responses of different external disturbances at different velocity levels and with different open draw lengths.

The results show that the radius of the roll has a significant effect on the web's behavior in terms of temporal length variation of the open draw. In this case, the open draw has non-constant boundary conditions, and thus the natural frequencies of the web depend on the length and tension distribution of the open draw. This phenomenon is accentuated especially in cases where the effect of the added mass (air mass) has been included in the model and in cases where the velocity of the web is high. One of the important dynamic phenomena revealed by the model is the rapid changing of web-roll contact points at both ends of the open draw. Due to this, longitudinal and transverse force components undergo rapid changes which could cause web breaks.

In the future, the main goal is to make experiments on the model in such a case where the web runs from roll to roll. One of our intentions is also to refine the model by a more realistic material assumption by taking into account the nonlinear behavior of the paper and also expanding the model in a third dimension. With aid of these steps, it is possible to obtain further information of time-dependent stress distributions on the web.