LaLaBand is the abbreviation for the German title "Simulation des Lateralen Laufverhaltens von schwach gespannten Prozessstahlbändern"
The primary aim of the project, funded by the Austrian research promotion agency FFG (grant number 861493), is the accurate simulation of the lateral run-off phenomenon that presents a severe hindrance for the operation of steel belt drives at low belt tension. No matter the particular application, the flawless function of steel belt drives always requires an active control system to guide the belt’s motion on the surface of the drums and to keep it from running off laterally (in direction of the drum axes). However, at low belt tension levels and, thus, increased sag the lateral run-off due to intrinsic imperfections of belt and machinery is intensified such that it becomes unmanageable with presently available controllers.
We develop an accurate simulation model for the operation of slack steel belt drives to gain insight into the mechanics of lateral run-off and to provide a solid foundation for improved control designs.
One step towards a digital twin for steel belt drives
The implementation of a numerical tool to simulate the operation of a steel belt drive system is challenging for several reasons: First, the material particles are performing a circumferential motion and, above that, sustain large transverse deflections as they pass through different domains (free strands & contact zones) in the course of one revolution. Secondly, the belt’s intrinsic geometric imperfections, which represent the primary source of lateral run-off, must be incorporated in a consistent manner. Lastly, the frictional contact with the drums as well as the extreme membrane stiffness of a thin steel belt in comparison to its flexural properties are difficult to handle numerically.
These primary obstacles are overcome by means of a purpose-built shell finite element model
- a mixed kinematic description of primary variables with resemblance to ALE that enables material flow in axial direction across the boundaries of the non-material finite element mesh
- the account for geometric imperfections by imposing intrinsic strains on the unshareble Kirchhoff-Love shell
- contact modelling in terms of an augmented penalty-regularisation technique
A series of physical experiments on an actual belt drive rig is conducted to validate the simulation
tool. Additionally, a rod finite element scheme is developed to supplement the computationally more
expensive shell model.
Figure: graphic abstract of the publication https://www.sciencedirect.com/science/article/pii/S0020740321003076, opens an external URL in a new window; published as Open-Access (CC BY 4.0)
Schmidrathner, Christian, Yury Vetyukov, and Jakob Scheidl. "Non‐material finite element rod model for the lateral run‐off in a two‐pulley belt drive, opens an external URL in a new window" ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik 102, no. 1 (2022): e202100135.
Scheidl, Jakob, Yury Vetyukov, Christian Schmidrathner, Klemens Schulmeister, and Michael Proschek. "Mixed Eulerian–Lagrangian shell model for lateral run-off in a steel belt drive and its experimental validation, opens an external URL in a new window" International Journal of Mechanical Sciences 204 (2021): 106572.