Pressure Distribution in Plate Rolling

Abstract

When analysing the stress distribution in the tool/workpiece interface in plate rolling, it is conventional to assume either Amontons friction law, τ = μp, or full stiction τ = k. Neither of these two laws are, however, generally valid. This paper presents an analysis by the slab method using a general friction model developed by Wanheim and Bay. The differential equation describing the pressure distribution in the roll gap is numerically solved on a computer using a fourth order Runge-Kutta method. Pressure and friction stress distributions as well as total load and torque are thereby estimated as functions of roll radius, initial plate thickness, reduction, friction factor, front tension, back tension and material stress strain hardening characteristic. Roll flattening is also taken into account. The results are in good accordance with experiments estimating the pressure distribution when rolling model material and load and torque when rolling aluminium. Especially the good torque predictions should be noticed since earlier analysis have failed at this point.