Spread in flat rolling

A velocity field was derived for a flat workpiece undergoing plastic deformation between cylindrical rolls in a rolling mill. Using the velocity field, an expression was written for the total power input required for the rolling process in terms of the process parameters: roll diameter, thickness reduction, workpiece geometry, surface friction, and spread. The Upper Bound Theorem was applied to the power expression to establish an upper limit on it. This limit was minimized with respect to spread to determine the value of spread requiring the least amount of input power.