Asymptotic Approach to the Hill Model of Spread in Rolling

摘要

A simplified procedure for the solution of the spread model proposed by Hill (1963) is presented for situations where the strip width is greater than the roll-gap length. The method utilizes a perturbation expansion for the width function and results in a simple analytical solution, overcoming the difficulties involved in solving the original complex, nonlinear, fourth-order differential equation. The solution provides insight into the relationship between the spread predicted and the roll gap parameters, and allows the assumptions made to be evaluated as leading order estimates to the stresses are produced.