Thesis (M.S.)--Rochester Institute of Technology, 1987. / Typescript. Includes bibliographical references (leaves 59-60).

Abstract Axially moving material problems are concerned with the dynamic response, vibration and stability of slender members which are in a state of translation. In Finland these are particularly important in the functioning of paper machines, in which out of plane vibration in the paper web, known as flutter, which from the point of view of mechanics is a phenomenon typical of an axially moving material, limits operation speeds and therefore the productivity of the machines. This subject links together a number of physical phenomena associated with aerodynamics, web movement, material behaviour and the geometry of the system. The aim of this research is to present a theoretical and numerical formulation of the nonlinear dynamic analysis of an axially moving web. The theoretical model is based on a mixed description of the continuum problem in the context of the dynamics of initially stressed solids. Membrane elasticity is included via a finite strain model, and the membrane transport speed through a kinematical study. Hamilton's principle provides nonlinear equations which describe the three-dimensional motion of the membrane. The incremental equations of Hamilton's principle are discretized by the finite element method. The formulation includes geometrically nonlinear effects: large displacements, variations in membrane tension and variations in transport velocity due to deformation. This novel numerical model was implemented by adding an axially moving membrane element to a FEM program which contains acoustic fluid elements and contact algorithms. This allowed analysis of problems including interaction with the surrounding air field and contact between supporting structures. The model was tested by comparing previous experiments and present nonlinear description of the dynamic behaviour of an axially moving web. The effects of contact between finite rolls and the membrane and interaction between the surrounding air and the membrane were included in the model. The results show that nonlinearities and coupling phenomena have a considerable effect on the dynamic behaviour of the system. The nonlinearities cause a noticeable stiffening of the membrane, and the vibration frequency of nonlinear system increases as the amplitude grows. At high values of transport velocity the first mode frequency passes over the second linear harmonic, and even the third. The results also show that the cylindrical supports have a distinct influence on the behaviour of an axially moving sheet. The boundary of the contact region clearly moves and weakens the nonlinear hardening phenomena that otherwise increase the fundamental frequency. This influence strengthens as the radius of the cylinders increases.

<p>Paper that is subjected to moisture undergoes dimensional changes. It expands during moistening and shrinks during drying. When the paper is under tension between rollers, the effects are complex since shrinkage and expansion are restricted in the width direction. Waves can then appear on the paper web. This can be a problem in heatset web offset printing. The problem is known as waviness or fluting. The printed papers exhibit a wavy shape, which is visually disturbing due to light reflections which create glossy streaks. The aim of the work described in this thesis was to develop a method suitable for studying the moisture- and tension-induced waviness. Experiments were carried out on a laboratory scale to study how such waves develop during moistening and drying. The experimental setup was based on a modified tensile tester. A CCD camera and image analysis based on the STFI-OptiTopo technique was used to characterise the waviness. Moistening and drying were achieved by changing the surrounding air humidity. The method was used to study the effect of moisture uptake by the paper, and to evaluate the effect of tension on the waviness. It was found that increasing moisture resulted in a higher waviness amplitude, but that the web tension controlled the wavelength of the waviness. A high tension gave rise to a shorter wavelength. The measured wavelength was compared with a previously suggested model and the predicted wavelength was about twice as high as the measured wavelength.</p> / <p>When paper becomes damp it can develop waves which can be a problem with heatset web offset printing. Paper with waves may have glossy streaks after printing. Laboratory experiments studied the effect of moisture uptake by the paper. Readings were taken at a range of air humidities. The effect of tension on the waviness was also measured. The waviness was characterised using a charge coupled device (CCD) camera and the STFI-Packforsk OptiTopo technique to analyse the images. When the humidity was increased the amplitude of the waves increased. A high tension resulted in shorter wavelengths. Results from a previous model were used as a comparison.</p>

Paper that is subjected to moisture undergoes dimensional changes. It expands during moistening and shrinks during drying. When the paper is under tension between rollers, the effects are complex since shrinkage and expansion are restricted in the width direction. Waves can then appear on the paper web. This can be a problem in heatset web offset printing. The problem is known as waviness or fluting. The printed papers exhibit a wavy shape, which is visually disturbing due to light reflections which create glossy streaks. The aim of the work described in this thesis was to develop a method suitable for studying the moisture- and tension-induced waviness. Experiments were carried out on a laboratory scale to study how such waves develop during moistening and drying. The experimental setup was based on a modified tensile tester. A CCD camera and image analysis based on the STFI-OptiTopo technique was used to characterise the waviness. Moistening and drying were achieved by changing the surrounding air humidity. The method was used to study the effect of moisture uptake by the paper, and to evaluate the effect of tension on the waviness. It was found that increasing moisture resulted in a higher waviness amplitude, but that the web tension controlled the wavelength of the waviness. A high tension gave rise to a shorter wavelength. The measured wavelength was compared with a previously suggested model and the predicted wavelength was about twice as high as the measured wavelength. / When paper becomes damp it can develop waves which can be a problem with heatset web offset printing. Paper with waves may have glossy streaks after printing. Laboratory experiments studied the effect of moisture uptake by the paper. Readings were taken at a range of air humidities. The effect of tension on the waviness was also measured. The waviness was characterised using a charge coupled device (CCD) camera and the STFI-Packforsk OptiTopo technique to analyse the images. When the humidity was increased the amplitude of the waves increased. A high tension resulted in shorter wavelengths. Results from a previous model were used as a comparison.