Abstract
A method of finding the distortion of the roll surface when subject to a known pressure distribution is described. This method is then combined with a plastic-flow theory of rolling to determine the shape of the arc-of-contact and the pressure distribution over it when neither of these are known beforehand. Apart from the assumptions inherent in the theory of plastic flow, two assumptions only have been made: that the roll is in a state of plane strain and that the shape of the arc-of-contact is independent of the distribution of the balancing forces. The accuracy of the results is estimated to be 20 per cent.
This paper shows that: first, it is not necessary to assume a parabolic pressure distribution to obtain a quantitative result; secondly, Hitchcock's solution (Hitchcock 1935)† is within the limits of error of the more fundamental solution and remains the most suitable method, for practical purposes, of allowing for roll flattening; thirdly, the main feature of the arc-of-contact is the depression in the region of peak pressure and the compensating greater curvature at both ends. This is a theoretical confirmation of Orowan's experiments (Orowan 1943).
Get full access to this article
View all access options for this article.