A rational analytical model of flat rolling problem

摘要

In the mechanics of metal forming processes (particularly in strip rolling), it is important to determine the load on the machine tool that deforms the material into a new shape, as well as to compute the velocity field, strain rates and stresses in the deformation zone. Since no exact solutions are available for such problems, the perturbation method with respect to the Bingham number (which emerges from the analysis of the governing equations) is proposed for solving the rolling problem in viscoplastic deformation. We determine the neutral point position, as well as the equations for the discontinuity surfaces limiting the deformation zone. It is of interest to note that the most widely accepted theory of rolling predicts the so-called friction hill type of normal stress distribution in the roll gap. The analysis shows that this model could predict wave-like distribution of the roll pressure. The model also predicts the key parameters such as load and torque as functions of the rolling parameters. The theoretical results are numerically exemplified, and the influence of various technological factors on the rolling process is discussed.