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The lateral deformations of webs in roll-to-roll (R2R) process machines can affect the quality of the manufacturing process. Webs can enter a cylindrical roller normally if the forces required to sustain normal entry and do not exceed the available friction forces. Webs with simple non-uniform length variation across their width (camber) will steer toward the long side, affecting the steady state lateral deformation and hence registration. Most previous studies have focused on tests and modeling a cambered web span in a free span between two rollers. Often these studies assume some displacement and slope boundary conditions are known and seek the remaining condition(s) that would dictate the steady state lateral deformation of the cambered web in the free span. In many spans in a process machine there may be no known boundary conditions and no steady state deformation of the cambered web. The web may travel toward the long side continually from one web span until the next until a web guide attempts to return the web to an acceptable lateral location in the process machine. The simplest case of multiple span cambered web lateral behavior is that of a cambered web belt transiting two aligned rollers which is the focus of the current work. Dynamic simulation (Abaqus/Standard) has been used to better understand the response of cambered webs under tension that has been witnessed in tests.
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Spatially Dependent Transfer Functions for Web Lateral Dynamics
In this paper we derive spatially dependent transfer functions for web span lateral dynamics which provide web lateral position and slope as outputs at any location in the span; the inputs are guide roller displacement, web lateral position disturbances from upstream spans, and disturbances due to misaligned rollers. This is in sharp contrast to the existing approach where only web lateral position response is available on the rollers. We describe the inherent drawbacks of the existing approach and how the new approach overcomes them. The new approach relies on taking the 1D Laplace transform with respect to the temporal variable of both the web governing equation and the boundary conditions. One can also obtain the web slope at any location within the web span with the proposed approach. A general span lateral transfer function, which is an explicit function of the spatial position along the span, is obtained first followed by its application to different intermediate guide configurations.
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- Award ID(s):
- 1635636
- PAR ID:
- 10025823
- Date Published:
- Journal Name:
- Proceedings of the Fourteenth International Conference on Web Handling
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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