Analysis of cross and vertical buckling in sheet metal rolling

Analysis of Longitudinal Buckling in Temper Rolling

“…In the previous study, 13) the material is in perfect contact with the roll during rolling. Thus, the analysis of buckling was performed using the residual stress of the material after rolling.…”

“…20) Thus, the normal stress components in a region that is sufficiently far from the material surface are expressed by the following equations, in consideration of Eqs. (9) and (13). (16) where P denotes the roll force per unit width acting on the material.…”

“…13) In the paper, when the buckling of the sheet is interfered with by the roll, it is assumed that cross buckling does not occur and that longitudinal buckling occurs.…”

“…(15). In the previous study, 13) since the material was in perfect contact with the roll at the cross section xϭ0, the plate was assumed to be built in at this cross section. In this study, however, since the material is hardly in contact with the roll at the cross section xϭ0, the plate is assumed to be simply supported at this cross section.…”

“…The author previously analyzed cross buckling and longitudinal buckling during cold rolling 13) by the elementary theory of buckling 10) and clarified that the shapes of the waves strongly depend on the front tension during rolling. Moreover, the wavelengths of the waves formed by cross buckling and longitudinal buckling and the angle between the direction of the crest lines of the waves formed by cross buckling and the rolling direction calculated are confirmed to closely coincide with those obtained in the experiment.…”