The Calculation of Roll Pressure in Hot and Cold Flat Rolling

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Abstract
A numerical or graphical method is given for computing, in strip or plate rolling, the distribution of roll pressure over the arc of contact and the quantities derived from this (e.g. the vertical roll force, the torque, and the power consumption). The method avoids all mathematical approximations previously used in the theoretical treatment of rolling, and permits any given variation of the yield stress and of the coefficient of friction along the arc of contact to be taken into account. It can be used, therefore, in both hot and cold rolling, provided that the basic physical quantities (yield stress and coefficient of friction) are known. The usual assumption that the deformation could be regarded as a locally homogeneous compression has not been made, and the inhomogeneity of stress distribution has been taken into account approximately by using results derived by Prandtl and Nádai from the Hencky treatment of two-dimensional plastic deformation. It is found that the discrepancy between the roll pressure distribution curves calculated from the Kármán theory and those measured by Siebel and Lueg is due to the assumption in the theory that the frictional drag between the rolls and the rolled stock is equal to the product of the roll pressure and the coefficient of friction. If frictional effects are dominant, as in hot rolling, this product may easily exceed the yield stress in shear which is the natural upper limit to the frictional drag, and then static friction, instead of slipping, occurs. This has been taken into account in the present method, and the calculated curves of roll pressure distribution show good agreement with the curves measured by Siebel and Lueg.

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