Winding virtual rolls

The winding of web materials is a subject of economic import that has resulted in mechanics analysis and model development. Many materials are wound into rolls for storage and subsequent processing. Winding is an accretive process in which the internal stresses within each layer of the wound roll are affected by the web layers that have been most recently added. As rolls wind, the edges take the approximate shape of an Archimedean spiral. All analyses and models to date have imposed the assumption that this spiral form can be replaced by a series of concentric web layers that are added one by one to the exterior of the model of the winding roll. It was also assumed that the bending stresses and strains associated with winding a flat web into a wound roll are negligible, an assumption with a validity that is highly dependent on web thickness. In this investigation, the web will be attached to a core and wound in a spiral form from the start to the completion of the wound roll. It will be shown that modeling the spiral geometry of the web in a wound roll can be beneficial in understanding stress concentrations in the vicinity of the starting position of the web on the core and for understanding how nip rollers can affect the web tension in the outer layer of a winding roll.