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Research Papers

# Analysis of the Effect of Strip Buckling on Stability of Strip Lateral Motion With Application to Cold Rolling of Steel

[+] Author and Article Information
T. Tarnopolskaya

CSIRO Mathematical and Information Sciences, Locked Bag 17, North Ryde, New South Wales 1670, Australiatanya.tarnopolskaya@csiro.au

D. J. Gates

CSIRO Mathematical and Information Sciences, GPO Box 664, Canberra, Australian Capital Territory 2601, Australiadavid.gates@csiro.au

J. Dyn. Sys., Meas., Control 130(1), 011001 (Dec 05, 2007) (7 pages) doi:10.1115/1.2807048 History: Received April 20, 2005; Revised March 27, 2007; Published December 05, 2007

## Abstract

A sudden loss of lateral stability (strip track-off) is a serious operational problem in cold rolling of steel that often leads to catastrophic consequences such as mill crashes and roll damage. This paper studies the causes of instability in lateral motion of a metal strip in a single span between the uncoiler and the first stand of a cold rolling mill. A mathematical model of strip lateral dynamics that includes a rolling mill model and a simplified physically based model of strip buckling is formulated. The numerical analysis of the model reveals that in the presence of strip buckling, the lateral motion becomes unstable once a critical level of asymmetry in rolling conditions is exceeded. The critical level of asymmetry increases with the increase in the tension applied to the strip. Below this critical level of asymmetry, a sudden transition to unstable motion occurs if a critical lateral deviation is reached. This paper demonstrates that the buckling of the strip can be responsible for lateral instability. The results of this paper explain the sudden onset of instability observed in metal rolling and the stabilizing effect of the tension applied to the strip, known in rolling practice.

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## Figures

Figure 1

Schematic of strip rolling: (a) strip in a span between the uncoiler and the reduction mill and (b) schematics of a four-high mill

Figure 2

Buckled regions according to Benson’s model

Figure 3

Comparison of nondimensional Benson’s curvature (solid curve) and the approximation (dashed curve)

Figure 4

Steady-state strip lateral deviations at the entry of the plastic region versus the level of asymmetry (FL−FR)∕FL for two different mean entry tensile stress: (1) 3MPa and (2) 22.3MPa

Figure 5

Strip off center as a function of time for scenarios with different initial off centers; the asymmetry in rolling conditions is represented by the differential roll force with (FL−FR)∕FL=0.2; the entry mean tensile stress is 22.3MPa

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