Pre‐Tensioned Belts Overhanging Elastic Rollers

Subject of this paper are deformation mechanisms in pre-tensioned elastic belts, which are wrapped around rollers carrying elastic layers that support the belts over part of their width. By means of analytical models and the finite element method the corresponding deformations of the belts are predicted. Special emphasis is put on the effects of the nonlinear (contact) boundary conditions in the vicinity of the lateral edges of the roller. The continuum finite element simulations provide reference solutions, and, furthermore, serve as an accurate means for predicting the contact stress distribution, whereas the semi-analytical solutions allow foran inexpensive and quick investigation of several parameter combinations. The high quality of the semi-analytical model can be judged by the excellent agreement of the obtained results with the reference finite element results. Pre-tensioned belts play an important role in production technology and in applications related to logistics. Usually, these belts are made of metals or polymers and show elastic behaviour in their range of operation. For the application of driving moments or forces as well as for supporting the belts, cylindrical rollers or drums are commonly used. In this study we look at a specifi c problem of belt-roller interaction: a roller, which is covered with an elastic layer, turns around an elastic belt, the width of which is greater than the width of the elastic layer. The belt is, therefore, overhanging the elastic layer. Because we deal with pre-tensioned belts, this leads to a radial displacement of the belt in regions where it is not supported by the layer. Since the displacement of the belt, which is driven by the tendency of the belt to attain a stress-free confi guration, is inhibited by the elastic layer, a strong mechanical interaction between the belt and the layer takes place. Over the better part of the roller, and especially a reasonable distance away from the edges of the layer, the belt is stretched over the layer leading to surface contact with a more or less uniform contact pressure distribution. Towards the edge of the elastic layer, which is fully covered by the belt, the contact situation becomes more complicated; the contact stress at the edge of the layer rises well above the expected uniform nominal pressure, indicating a stress concentration at the layer edge. The prediction of this elevated contact stress domain is one of the subjects of this study as it is relevant for the assessment of the stress state with respect to, e.g., the fatigue resistance of a moving metal belt.