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Application of Buckingham Π ‐theorem to asymmetric plate rolling processes
Author(s) -
Münker Tobias,
Anders Denis,
Weinberg Kerstin
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210312
Subject(s) - dimensionless quantity , slab , buckingham , curvature , parametric statistics , mechanics , finite element method , boundary value problem , materials science , structural engineering , mathematics , physics , geometry , engineering , mathematical analysis , statistics , quantum mechanics
Rolling under asymmetrical conditions such as temperature gradients within the material, difference of the circumferential velocity of the rolls and different friction coefficients cause the rolled slab to bend towards the direction of one of the rolls. In general this effect is undesired, since it hinders the further material transport and is a potential danger for the machine components in the proceeding processes. Unfortunately the essential mechanisms and the sensitivity of the influencing parameters in asymmetric rolling are still not comprehended sufficiently. Here a novel approach is presented in order to gain an enhanced insight into the front‐end bending phenomenon. To this end Buckingham Π‐theorem is applied to recover dimensionless coefficients describing the state of the roll gap and enable a reduction of the number of calculations in the required parametric studies. These parametric studies have been performed applying a finite element model considering elasto‐plastic material behaviour and the boundary conditions applied to the slab in the roll gap. The dimensionless quantity taking into account the slab's curvature is thoroughly investigated in terms of the other dimensionless system parameters. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)