Third-power spline function strip element method and its simulation of the three-dimensional stresses and deformations of cold strip rolling

A new method called the third-power spline function strip element method for simulating the three-dimensional stresses and deformations of cold strip rolling is presented. The rolling deformation zone is divided into a number of strip elements. The transverse distribution model of the lateral displacement on the strip element is constructed to be third-power spline function, and the longitudinal distribution model of it is reconstructed to be a quartic plus cubic function. The three-dimensional stresses and deformations in the deformation zone are formulated. The frictional stresses are calculated from the Coulomb friction law in the sliding zones and from preliminary displacement theory in the adhesion zone. On the conditions of a width to thickness ratio of 625 of strip and different rolled strip shapes, the three-dimensional mechanics behavior of the cold strip rolling on a 4-high mill is simulated by this method, the simulated results agreeing with the experimental ones well. The work of this paper is of great importance to the development of the three-dimensional rolling theory of strip, the shape theory and the shape control technology of strip.