Slip Line Field Solution for Second Pass in Lubricated 4-High Reversing Cold Rolling Sheet Mill
Oluleke O. Oluwole, Olayinka Olaogun
.

Abstract

The development of a possible slip line field (slf) for theoretical calculations of the deforming pressure (load) in a second pass of a lubricated cold rolling sheet mill and validation using values from an aluminium sheet rolling mill was done in this work. This will be relevant in the manufacturing industries providing an easy method for determining necessary applied rolling load. Experimental rolling was carried out to observe the shear lines in the deformation field. Construction of possible slip line field model was developed adhering strictly to assumptions of rigid plastic model. Calculation of the deforming force/load was achieved using Hencky’s equation. Results showed that the load calculations for constructed slip line field using aluminium sheet rolling as an example tallied with values obtained from Tower Aluminium rolling mill. Slip line fields constructed for the second pass described adequately the rolling pressure in the cold rolling process, giving a valid solution of the exact load estimates on comparison with the industrial load values. Roll pressure along the arc of contact rose fairly linearly from the entrance to a maximum at the exit point. This work showed that slf for the first pass in a cold rolling mill cannot be used for subsequent passes; it requires construction of slfs for each pass in the cold rolling process.

Share and Cite:

O. Oluwole and O. Olaogun, "Slip Line Field Solution for Second Pass in Lubricated 4-High Reversing Cold Rolling Sheet Mill," Engineering, Vol. 3 No. 12, 2011, pp. 1225-1233. doi: 10.4236/eng.2011.312152.

Conflicts of Interest

The authors declare no conflicts of interest.

 [1] T. Von Karman, “On the Theory of Rolling,” Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 5, 1925, pp. 130-141. [2] E. Orowan, “The Calculation of Roll Pressure in Hot and Cold Flat Rolling,” Proceedings of the Institue of Me- chanical Engineering, Vol. 150, 1943, pp. 140-167. [3] A. Nadal, “The Force Required for Rolling Steel Strip under Tension,” Journal of Applied Mechanics ASME, Vol. 61, 1939, A54-A62. [4] D. R. Bland and H. Ford, “The Calculation of Roll Force and Torque in Cold Strip Rolling with Tensions,” Proceedings of the Institute of Mechanical Enigineering, Vol. 159, No. 1, 1948, pp. 144-163. doi:10.1243/PIME_PROC_1948_159_015_02 [5] R. B. Sims, “The Calculation of Roll Force and Torque in Hot Rolling Process,” Proceedings of the Institue of Mechanical Engineering, Vol. 168, No. 1, 1954, pp. 191-200. doi:10.1243/PIME_PROC_1954_168_023_02 [6] J. M. Alexander, “A Slip Line Field for Hot Rolling Process,” Proceedings of the Institute of Mechanical Engineering, Vol. 169, No. 1, 1955, pp. 1021-1030. doi:10.1243/PIME_PROC_1955_169_103_02 [7] T. C. Firbank and P. R. Lancaster, “A suggested slip- line field for cold rolling with slipping friction,” Interna- tional Journal of Mechanics of Science, Vol. 7, No. 12, 1965, pp. 847-852. [8] T. C. Firbank and P. R. Lancaster, “A Suggested Slip-Line Field for Lubricated Cold Rolling,” International Journal of Mechanics of Science, Vol. 9, No. 2, 1967, pp. 65-67. doi:10.1016/0020-7403(67)90044-6 [9] I. F. Collins, “Slip Line Field Solutions for Compression and Rolling with Slipping Friction,” International Journal of Mechanics of Science, Vol. 11, No. 12, 1969, pp. 971-978. doi:10.1016/0020-7403(69)90009-5 [10] P. Dewhurst and I. F. Collins, “A Matrix Technique for Constructing Slip-Line Field Solutions to a Class of Plane Strain Plasticity Problems,” International Journal for Nu- merical Methods in Engineering, Vol. 7, No. 3, 1973, pp. 357-378. doi:10.1002/nme.1620070312 [11] M. Salimi and M. Kadkhodaei, “Slab Analysis of Asymmetrical Sheet Rolling,” Journal of Materials Processing Technology, Vol. 150, No. 3, 2004, pp. 215-222. doi:10.1016/j.jmatprotec.2004.01.011 [12] R. Hill, “The Mathematical Theory of Plasticity,” 1st Edition, Oxford University press, Oxford, 1950. [13] B. Avitzur, “Metal Forming: The Application of Limit Analysis,” Marcel Dekker, Inc. New York, 1980. [14] N. R. Chitkara and M. A. Butt, “Combined Rod and Tube Extrusion: Numerical Solution of Axi-Symmetric Slip- Line Fields and Associated Velocity Fields,” International Journal of Mechanical Sciences, Vol. 39, No. 4, 1997, pp. 435-454. doi:10.1016/S0020-7403(96)00038-0 [15] N. Fang and P. Dewhurst, “Slip-Line Modeling of Built-Up Edge Formation in Machining,” International Jour- nal of Mechanical Sciences, Vol. 47, No. 7, 2005, pp. 1079-1098. doi:10.1016/j.ijmecsci.2005.02.008 [16] W. S. Weroński, A. Gontarz and Z. B. Pater, “Analysis of the Drop Forging of a Piston Using Slip-Line Fields and FEM,” International Journal of Mechanical Sciences, Vol. 39, No. 2, 1997, pp. 211-213, 215-220. doi:10.1016/0020-7403(96)00055-0 [17] K. Mori, K. Osakada and T. Oda, “Simulation of Plane-Strain Rolling by the Rigid-Plastic Finite Element Method,” International Journal of Mechanical Sciences, Vol. 24, No. 9, 1982, pp. 519-527. doi:10.1016/0020-7403(82)90044-3 [18] J. Synka and A. Kainz, “A Novel Mixed Eulerian-La- grangian Finite-Element Method for Steady-State Hot Rolling Processes,” International Journal of Mechanical Sciences, Vol. 45, No. 12, 2003, pp. 2043-2060. doi:10.1016/j.ijmecsci.2003.12.008 [19] J. Chakrabaty, “Theory of Plasticity,” 3rd Edition, Elsevier, Butterworth-Heinemann, Oxford, 2006. [20] M. Konyaeva, “Fundamentals of the Theory of Plasticity,” 1st Edition, Mir Publishers Moscow, Moscow, 1974.