Title: Mixed Eulerian–Lagrangian shell model for lateral run-off in a steel belt drive and its experimental validation
Language: English
Authors: Scheidl, Jakob 
Vetyukov, Yury 
Schmidrathner, Christian 
Schulmeister, Klemens 
Proschek, Michael 
Category: Original Research Article
Issue Date: 15-Aug-2021
Citation: 
Scheidl, J., Vetyukov, Y., Schmidrathner, C., Schulmeister, K., & Proschek, M. (2021). Mixed Eulerian–Lagrangian shell model for lateral run-off in a steel belt drive and its experimental validation. International Journal of Mechanical Sciences, 204, 1–18. https://doi.org/10.1016/j.ijmecsci.2021.106572
Journal: International Journal of Mechanical Sciences 
ISSN: 0020-7403
Abstract: 
A non-material shell finite element model is developed and applied to the example problem of a slack steel belt moving on two rotating drums. For the first time in the open literature we demonstrate an approach for predicting the time evolution of the lateral run-off velocity of the belt in response to its geometric imperfection and angular drum misalignment. We adopt a novel Eulerian–Lagrangian kinematic description featuring a mixed parametrisation of the configurational space with a Eulerian circumferential coordinate and two Lagrangian coordinates for the transverse and lateral deflections. A nonlinear finite element approximation provides the necessary C1 inter-element continuity in this compound coordinate system. Using the model of elastic tangential contact, we account for the convective term in the local increments of the relative displacement between the contacting surfaces during the time integration. A thorough convergence study with respect to the mesh and time step sizes justifies the approach. Together with the successful validation against the results of a series of physical experiments, this makes the present contribution an important step towards a model-based controller design.
Keywords: belt drive mechanics; elastic contact; finite element analysis; Kirchhoff shell; Mixed Eulerian–Lagrangian description; transient analysis
DOI: 10.1016/j.ijmecsci.2021.106572
Organisation: E325-02 - Forschungsbereich Mechanik fester Körper 
License: CC BY 4.0 CC BY 4.0
Publication Type: Article
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