Analysis of flow and stresses in flattening a circular tube by rolling

Circular metal tubes are flattened to increase the tube surface-to-cross-sectional flow area, for use mainly in heat exchangers to enhance the rate of heat transfer. In the present work an analytical solution is obtained for the problem of cold flattening of a round tube into an oblong shape through rolling between two flat rolls. A velocity field is formulated to yield the strain-rate components from which the stress components are obtained by substituting in the flow rule and integrating the equations of equilibrium. The solution predicts section geometry, roll surface pressure distribution, roll load and rolling torque. The results obtained show that the tube wall is subjected to biaxial membrane and bending stresses. For the same tube diameter and height reduction the roll load and torque are proportional to the tube wall thickness.