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

Akash Patel, Arif Malik, Ritin Mathews

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Introduced is a new physics-based three-dimensional (3D) mathematical model capable of efficiently predicting time histories of the nonlinear structural dynamics in cold rolling mills used to manufacture metal strips and sheets. The described model allows for the 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 a 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 the 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 the inability to model clustertype 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 s and 3.38 s per time-step, respectively.

Original languageEnglish
Article number071009
JournalJournal of Manufacturing Science and Engineering
Volume144
Issue number7
DOIs
StatePublished - Jul 2022
Externally publishedYes

Funding

The authors gratefully acknowledge support for this work from the National Science Foundation (Grant No. CMMI-1555531).

Keywords

  • cold rolling
  • flatness
  • mathematical model
  • strip thickness profile
  • structural dynamics
  • time history

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