On the measure of nonflatness of rolled strips and sheets

Numerical analysis and correct measurements of the nonflatness parameters of rolled steel strips and sheets is a quite complicated problem regularly solved by the employees of rolling mills. Consumers of steel sheets impose their requirements for the flatness of sheets according to GOST 19903-2015 (hot-rolled) and GOST 19904-90 (cold-rolled) specifying the deviations from flatness, i.e., the maximum distance between the surface of a finished steel sheet laid on a calibration plate and a ruler 1 m in length attached to it. In the process of rolling, the nonflatness of steel strips is automatically computed according to the difference between the elongations of the edge and middle parts of the strip and measured in the units called “I-Units.” We present the results of theoretical analysis of the measure of nonflatness of steel strips/sheets for various methods of approximation of their shapes. It is shown that the proposed formula guarantees an almost threefold improvement of the formula presented in the fundamental work by Yu. D. Zheleznov “Rolling of Flat Sheets and Strips.”