Effective modeling of cold rolling of metals

In this work, we extended an existing version of the Flow-Line Model (FLM) to the symmetric cold rolling of technically pure aluminum sheets. Through the modifications, the rolling process can be described with improved precision even in special conditions. The FLM aims to approximate the velocity values at each point of the rollgap using the new analytical function. The difficulty of the FLM models is in finding the correct value of the parameters based on the geometrical dimensions and frictional conditions. Besides the theoretical changes to the model, a set of empirical parameters were introduced, and the equations to determine the value of these empirical parameters were built up based on numerical results of Finite Element Model (FEM) simulations for a wide range of geometrical parameters.

The main theoretical challenge is to approximate the rollgap using a proper function. The distribution of the shear strain rates along the sheet’s thickness was approximated by a power function. The newly introduced empirical parameters were determined by using three non-dimensional factors: (i) the ratio of the actual to minimal coefficient of friction, (ii) the relative reduction in the sheet’s thickness, and (iii) a geometrical ratio expressing the ratio of the rollgap’s length to the sheet’s thickness.

The model was tested for the following regimes of the non-dimensional factors: the thickness reduction was changed from 0.01 to 0.38; the ratio of the pressed arc to the radius was varied between 0.0082 and 0.31; and the ratio of the real to minimal coefficient of friction was changed from 1.05 to 2.5.

The model’s precision determined from the three measured distortion lines (generated by Vickers indentations) was compared to their simulated version.