Leveling is a process used to minimize the plate defects including flatness imperfections and uniformity of internal stress in the plate industry. It plays an important role in delivering the desired material properties and product standards required. This paper presents a new analytical method for the curvature analysis of plate during the leveling process. The explicit expressions of the curvature integration model were derived in detail by an assumption of ignoring the residuals stress superimposed effect (IRSSE). The curvature analysis procedure was given about how to choose different expression to build the explicit curvature integration equations which were solved with fsolve function in Matlab. The contact angles and bending curvatures could be firstly analyzed in 0.7–0.8 second even though with random initial values. Then, they were initialized to the procedure by considering the residual stress effect and it only needed 3–4 seconds in 2 iteration steps to get the final solution. It was found that the result by IRSSE is close enough to the solution of the method by considering residual stress effect (CRSSE). The curvature and trajectory distribution by IRSSE and CRSSE just reflects on the last leveling areas because of the residual stress accumulative error effect. The analytical methods by IRSSE and CRSSE have the advantage of iteration speed and solution accuracy, respectively. Therefore, the proposed combined method is potential to the future roller intermeshes optimization research.

Leveling process is usually used to minimize the plate defects including flatness imperfections and uniformity of internal stress in the plate industry. Roller intermeshes are important parameters in the leveling process to ensure the high-quality leveled plate. Some current researches treat the plate as a simple beam and ignore the stress superimposed effect to study how to set the roller intermeshes. This article presents an analytical optimization model to search the optimal entry and exit intermeshes for each incoming plate with consideration of the relationship between the roller intermeshes and bending curvatures during the whole leveling process. The optimization model was solved and the results were verified with production data. The relationship between the optimal roller intermeshes and plate thickness, yield stress, and Young’s modulus were discussed in details. It was found out that the roller intermeshes can be set the same for different incoming plates but with equal elastic limit curvature. A four-dimensional database of optimal roller intermeshes about different elastic limit curvature, expected plastic strain ratios, and roller spaces was built. The roller intermeshes can be quickly tracked in less than 1 s as long as the thickness, yield stress, and Young’s modulus of incoming plate and roller space are given according to the database so that it can be used effectively on the leveling production line.