"Steady-State Simulation of Flat Rolling Processes - A Novel Mixed Eulerian-Lagrangian Approach with Applications to Plane Strain Problems"
Steady-State Simulation of Flat Rolling Processes - A Novel Mixed Eulerian-Lagrangian Approach with Applications to Plane Strain Problems
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The present study in this Ph.D. thesis is concerned with the mathematical modelling and numerical simulation of steady-state metal forming processes under plane strain conditions, in particular with the hot rolling of steel
slabs. A novel mathematical model based on a new formulation in the mixed Eulerian-Lagrangian co-ordinate system is derived, which allows for a straightforward and matrix-structure preserving implementation of displacement
Its implementation into a new numerical code based on the finite element method will be outlined. Due to the special form of the weak formulation of the governing equations related to this new model, such as the solving for a velocity component (v) in longitudinal but a displacement
component (u) in vertical direction and the occurrence of friction, special techniques had to be utilised in the code. For the purpose of verification and better comparison of the results obtained with this new model - for obvious reasons briefly denoted as vu-model hereafter - we also
implemented a more standard-like and solely velocity-based model (vv-model), which is originally framed in Eulerian co-ordinates and then transformed to the mixed Eulerian-Lagrangian space.
The numerical results obtained with the new model for hot rolling processes involving thin strips and a nearly homogeneous deformation are then verified against results obtained with a simplified slab model, which is based on the Karman-Siebel differential equations and provides a good approximation for (nearly) homogeneous deformation cases, and also against the velocity-based vv-model. Several modifications for this test case are studied and grid independence checks are performed before the new model is applied to more complex real-world problems of hot rolling processes for metal products, ranging from thick strips to thick slabs. Deformations of these products are
studied up to the maximum draft (thickness reduction) possible...