Efficient Three-Dimensional Model to Predict Time History of Structural Dynamics in Cold Rolling Mills

Abstract

Introduced is a new physics-based 3D mathematical model capable of efficiently predicting time histories of the nonlinear structural dynamics in cold rolling mills used to manufacture metal strip and sheet. The described model allows for prediction of transient strip thickness profiles, contact force distributions, and roll-stack deformations due to dynamic disturbances. Formulation of the new 3D model is achieved through combination of the highly-efficient simplified-mixed finite element method with a Newmark-beta direct time integration approach to solve the system of differential equations that governs motion of the roll-stack. In contrast to prior approaches to predict structural dynamics in cold rolling, the presented method abandons several simplifying assumptions and restrictions, including 1D or 2D linear lumped parameter analyses, vertical symmetry, continuous and constant contact between the rolls and strip, as well as inability to model cluster-type mill configurations and accommodate typical profile/flatness control mechanisms used in industry. Following spatial and temporal convergence studies of the undamped step response, and validation of the damped step response, the new model is demonstrated for a 4-high mill equipped with both work-roll bending and work-roll crown, a 6-high mill with continuously-variable-crown (CVC) intermediate rolls, and finally a complex 20-high cluster mill. Solution times on a single computing processor for the damped 4-high and 20-high case studies are just 0.37 seconds and 3.38 seconds per time step, respectively.

Influence of work-roll grinding error and high-fidelity corrective grinding in cold sheet rolling

“…Considering first Fig. 5a, the results shown help reveal the transfer characteristics by eliminating the influences of bulk body deformation 1 . This is because at any transverse distance from mill center, the exit thickness profiles in the earlier Fig.…”

“…On account of applicability to complex mill configurations (e.g., 20high cluster mills [27]), as well as computational cost and accuracy requirements, the physics-based simplified mixed finite element method (SM-FEM), introduced in [24] and adapted with an advanced contact algorithm to accommodate both low order and high-fidelity roll profiles [20,23,28,29], is adopted herein. Although the SM-FEM model described can be coupled with a Newmark-beta time integration technique to simulate temporal behavior of the 3D roll-stack and predict transient evolution of the rolled strip profile (as described in [1]), a static model is sufficient for the investigations in this work.…”

“…, the same roll when warm (after a single old rolling pass), and the same roll when cold and worn (after multiple passes); (d) section of a thin strip showing complex flatness (shape) defects. [1] The dimensional quality of rolled strip, as influenced by the foregoing factors, is broadly addressed in terms of thickness profile and flatness (or shape), although the two are interdependent due to mass conservation. In the cold rolling of thin metals in particular, widthwise expansion of strip or sheet is negligible.…”

“…Fig. 1 (a) 4-high rolling mill stand; (b) Exaggerated natural mill deflection behavior of 4-high mill stand, involving bending, shear, and flattening of rolls; (c) Measured roll diameter profiles for a new work roll, the same roll when warm (after a single old rolling pass), and the same roll when cold and worn (after multiple passes); (d) section of a thin strip showing complex flatness (shape)defects [1]. …”