The Minimum Gauge Problem in Thin Strip Rolling

All previous analyses of the minimum gauge problem either fail to arrive at a criterion for determination of the minimum gauge or result in predictions which are grossly in error. The basic assumptions utilized in these analyses are investigated in the present work with a view toward improving the existing theories. Those assumptions whose validity appears questionable are considered in detail through appropriate analysis. In particular, these assumptions are: (i) the strip and rolls deform uniformly across the width of the strip; (ii) Coulomb (sliding) friction occurs between the rolls and strip. Theoretical treatment of the complex three-dimensional behavior of the rolls and strip is made tenable through simplifications to suitable two-dimensional problems. The primary result of the investigation indicates that the assumption of sliding friction is completely without justification in rolling at the limiting conditions. A new shear traction distribution is postulated which is consistent with the fundamental laws of friction and results in sticking friction (zero slip) over most of the contact region. Incorporating this shear distribution, limiting rolling conditions can be shown to exist theoretically and the minimum gauge can be predicted. It is also found that the Poisson’s ratio must be one-half in the regions of incipient plastic yielding in the strip if a minimum gauge is to be predicted.