Numerical Simulation of Tension Losses and Reaction Forces in Tension Levellers

A hierarchy of different simulation models for the tension levelling process was developed for the prediction of the key process results (including strip bending line, strip elongation, roll reaction forces, required level of tension, tension losses as well as power requirements of the drives). Finite Element simulations based on commercial FEM packages are particularly challenging, as locally pronounced elasto-plastic deformations occur simultaneously at concentrated regions of contact between strip and several bending rolls, leading to simulation models with a large number of degrees of freedom, and – in combination with the highly non-linear characteristics of contact, material and geometry – to excessive computational efforts even on modern mainframes. To overcome the unacceptable computational costs of such FEM simulations, an alternative modelling approach, based on the Principle of Virtual Work and a specialised “Arbitrary Lagrangian-Eulerian” (ALE) formalism was elaborated. The novel concept is based on “parametric shape functions” (PSF) that describe both geometry and strain distribution of the deformed strip. Compared to FEM-models developed in commercial software packages, the new PSF model exhibits a drastic reduction of degrees of freedom and computational costs and simultaneously maintains high agreement of the key results under consideration.