New Numerical Solution of von Karman Equation of Lengthwise RollingReport as inadecuate

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Journal of Applied Mathematics - Volume 2015 2015, Article ID 843720, 20 pages -

Research Article

Alexander Dubček University of Trenčín, Pri Parku 19, 911 06 Trenčín-Záblatie, Slovakia

Technical University of Košice, Faculty of Metallurgy, 042 00 Košice, Slovakia

Received 10 June 2015; Accepted 16 August 2015

Academic Editor: Sutasn Thipprakmas

Copyright © 2015 Rudolf Pernis and Tibor Kvackaj. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The calculation of average material contact pressure to rolls base on mathematical theory of rolling process given by Karman equation was solved by many authors. The solutions reported by authors are used simplifications for solution of Karman equation. The simplifications are based on two cases for approximation of the circular arch: a by polygonal curve and b by parabola. The contribution of the present paper for solution of two-dimensional differential equation of rolling is based on description of the circular arch by equation of a circle. The new term relative stress as nondimensional variable was defined. The result from derived mathematical models can be calculated following variables: normal contact stress distribution, front and back tensions, angle of neutral point, coefficient of the arm of rolling force, rolling force, and rolling torque during rolling process. Laboratory cold rolled experiment of CuZn30 brass material was performed. Work hardening during brass processing was calculated. Comparison of theoretical values of normal contact stress with values of normal contact stress obtained from cold rolling experiment was performed. The calculations were not concluded with roll flattening.

Author: Rudolf Pernis and Tibor Kvackaj



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