An upper bound method for analysis of three-dimensional deformation in the flat rolling of bars

3D Analysis of cold rolling using a constitutive model for interface friction

“…Thus, Komori [4] has used a 3D upper bound method and has compared with experiments [25] carried out for lead, rolled between perfectly rough rolls. These results show that for R=h 0 =21:3; h=h 0 =0:6 and w 0 =h 0 = 4 the width spread is 16% according to the model and 25% according to the experiments.…”

“…Zhang [3], have focus on two-dimensional deformation, the upper bound, e.g. Komori [4], and the ÿnite element method, e.g. [5][6][7][8][9][10][11], have been used for two-dimensional as well as three-dimensional studies of the rolling process depending on the assumption for the deformation of the work piece material in the width direction.…”

“…Whether the plane strain assumption used in 2D rolling analyses is a reasonable approximation highly depends on the width-to-thickness ratio of the work piece, as the width spread during the rolling process increases with decreasing width-to-thickness ratio, e.g. [4], Micari [6]. However, for rolling processes symmetrical with respect to the middle plane of the width the results for the symmetry plane obtained by a 3D rolling analysis coincide with the results of the corresponding 2D rolling analysis in cases where the width is much larger than the plate thickness, e.g.…”

“…For at rolling of plate, slab or thick strip either purely slipping contact, [6], Lin and Lin [10], Lee [11], or a combination of both slip and no-slip, [7], Richelsen [8,9], have been used for the description of the interfacial contact between the roll and the work piece. While 2D studies of the rolling process are reported in [1][2][3]8,9], the results shown in [7] are for both 2D and 3D studies, and results for 3D studies of the rolling process are given in [4][5][6]10,11]. However, for the 3D studies it is not in all cases clear how the friction force vector at the two-dimensional interface between the roll and the work piece is described and included in the analyses, e.g.…”

“…However, for the 3D studies it is not in all cases clear how the friction force vector at the two-dimensional interface between the roll and the work piece is described and included in the analyses, e.g. [4,6]. Also 3D studies where the friction force in the transverse rolling direction has been neglected are given in the literature, e.g.…”