Analysis of edge rolling based on continuous symmetric parabola curves

Edge rolling plays a vital role in width control of strip rolling, where plastic deformation concentrates in the edge of the slab. Then, the center of the slab remains its initial shape. The local deformation is different from overall one which obtained in horizontal rolling. In this paper, dog-bone shape is creatively described by a continuous symmetric parabola used to describe, and based on the complex mathematical function, a kinematically admissible continuous velocity field for edge rolling is established. Finally, the upper deformation power function is yielded. Based on minimum of the power, the results in edge rolling force and torque are obtained. Some vertical rolling forces for copper and aluminum experiments are calculated by the function, and then, also the results are verified by the traditional models. Anyway, the maximum error is less than 18 %. This is a crossover study on both mathematical curve and mechanical analysis which can be seen as a combination of the theory and engineering.