Publication Date


Document Type


Committee Members

Ramana Grandhi (Advisor)

Degree Name

Doctor of Philosophy (PhD)


This work presents improved technology for attaining high-quality rolled metal strip. The new technology is based on an innovative method to model both the static and dynamic characteristics of rolling mill deflection, and it applies equally to both cluster-type and non cluster-type rolling mill configurations. By effectively combining numerical Finite Element Analysis (FEA) with analytical solid mechanics, the devised approach delivers a rapid, accurate, flexible, high-fidelity model useful for optimizing many important rolling parameters. The associated static deflection model enables computation of the thickness profile and corresponding flatness of the rolled strip. Accurate methods of predicting the strip thickness profile and strip flatness are important in rolling mill design, rolling schedule set-up, control of mill flatness actuators, and optimization of ground roll profiles. The corresponding dynamic deflection model enables solution of the standard eigenvalue problem to determine natural frequencies and modes of vibration. The presented method for solving the roll-stack deflection problem offers several important advantages over traditional methods. In particular, it includes continuity of elastic foundations, non-iterative solution when using pre-determined elastic foundation moduli, continuous third-order displacement fields, simple stress-field determination, the ability to calculate dynamic characteristics, and a comparatively faster solution time. Consistent with the most advanced existing methods, the presented method accommodates loading conditions that represent roll crowning, roll bending, roll shifting, and roll crossing mechanisms. Validation of the static model is provided by comparing results and solution time with large-scale, commercial finite element simulations. In addition to examples with the common 4-high vertical stand rolling mill, application of the presented method to the most complex of rolling mill configurations is demonstrated with an optimization example involving the 20-high Sendzimir mill.

Page Count


Department or Program

Ph.D. in Engineering

Year Degree Awarded


Included in

Engineering Commons