Extended model for the prediction of boundary and hydrodynamic friction in cold rolling using a modular concept of models
Sprache des Titels:
Metec InSteelCon 2011 Proceedings
An extended model for the evolution of strip surface roughness and friction along the roll bite in cold rolling is presented. The model is based on the assumption that periodic roughness structures (e.g. triangles) characterised by longitudinal and transversal components exist. The evolution of contact area in both rolling direction and strip width direction is predicted using a combination of Sutcliffe?s as well as Wilson and Sheu?s theories for the respective idealized cases (purely transversal or purely longitudinal roughness structures). Lubricant pressure, which is influenced by the length-to-width ratio of the roughness structures, is governed by hydrodynamic mechanisms. The contact area is modelled as surface in 3D and may exhibit different geometrical properties in length and width directions. A locally distributed coefficient of friction is evaluated, which is composed of the area-weighted contributions of lubricant-dominated friction and friction at the boundary contact area and from which a globally averaged coefficient of friction is derived.
A thermodynamic sub-model is included in order to incorporate the effects of temperature increase on the properties of the lubricant, which is caused by plastic strip deformation, shear and compression in the lubricant film and by boundary contact shear stresses. A modular and hierarchical implementation strategy based on well-defined interfaces between the respective modules of models is chosen to facilitate possible further enhancements of sub-models. To solve the underlying coupled differential and algebraic equations (DAE-system), non-dimensional variables are introduced ensuring a well-conditioned system. By spatial discretization along the arc of contact, the problem can be reduced to a set of highly non-linear coupled algebraic equations, which are solved simultaneously by utilizing a variant of the well-known Newton-Raphson algorithm. Some selected results will be presented and discussed in the paper.