If a web laying on a plane surface does not have a perfectly flat and straight shape, it has camber. The cambered web laying on the plane surface that flattens but forms a curved shape has a uniform camber; the cambered web that has does not flatten on the plane and forms a baggy lane or edges has local cambers . Cambered webs have severe steering issues as handled on the web line.
We developed an implicit dynamic FE model and studied the deformation of cambered web with uniform curvature transporting on web line and the boundary conditions in the final steady state. The web camber was modeled by an initial linearly varied thermal expansion over width of the web, which was implemented by a spatial temperature field defined by the Abaqus user subroutine UTEMP. We found cambered web steers to its longer side and ultimately forms a S-shape in the span.
The reason of using implicit dynamic analysis type over explicit dynamic is, first, implicit dynamic analysis provides cleaner displacement results while the default explicit dynamic analysis has more noise; second, the subroutine which directly assigns a spatial temperature field is only available in Abaqus/Standard. There is no quick way to implement this in Abaqus/Explicit.
Sometimes in a modeling and analysis work, successfully simulating a problem is not easy, successful interpretation of results is harder. The latter requires a solid theoretical knowledge, a close experience of the physical problem, and the intuition formed by both. As a thorough understanding of problem is gained, articulation and representation of the understanding is also hard. Most of the finite element codes are focusing on improving the algorithm part, which is tries to provide a better tool to simulate more physical problems, accurately and efficiently. The post-processing part of those codes, which helps to articulate and represent our understanding, lags far behind. In this problem I developed a little Python script that can extract relevant data from ODBs of Abaqus and visualize them. Most of the time for the cambered web problem, the middle line of the cambered web can represent the movement and deformation of the web. So I specifically visualized the lateral displacement, slope, and curvature of the middle line of the cambered web between the two rollers (blue and red in the animated figures below). I think this helps us to intuitively “see” the deformation and boundary conditions related with beam theory.
We also simulated the cambered web transporting on 3 rollers that steers on 2 spans and the cambered belt problem.
- J. J. Shelton, “Effects of Web Camber on Handling”, Proceedings of the Fourth International Conference on Web Handling, Stillwater, OK, 1997