The article presents the results of development and research of technological schemes of planting flanges on tubular (ring) workpieces by stamping by rolling cylindrical and conical rolls. It is shown that the achievement of significant dimensions of the various elements of the workpiece is possible by providing a directed flow of metal by changing the relative position of the roll and the workpiece. Planting of external flanges is one of the most effective operations of stamping by rolling, as it allows you to form a wide range of products with advanced geometric elements. To assess the technological capabilities of the flange landing operation, the most dangerous from the destruction positions of the workpiece zone was identified and the analysis of the stress strain state of the material using the method of grids, hardness measurement and microstructural analysis. According to the results of the research, the ways of deformation of the particles of the material of the peripheral surface of the flange in the coordinates "intensity of deformations - an indicator of the stress state" are schematically constructed. These deformation paths are given against the background of curves of ultimate deformations of steels, which are built on the results of uniaxial compression and torsion of cylindrical specimens and using tested approximations. A mathematical model of deformation trajectories is constructed, for which a one-parameter function is taken as a basis, which is "glued" from the elementary function of the sine and tangent to it at some point in the line. To determine the used plasticity resource, a damage summation model with a power approximation of the damage function was adopted. As a result, we have for the first time described the general expression of the linear damage summation model for the case of the parametric deformation path problem. The graphical representation on the constructed model of accumulation of damages in material of a dangerous zone of a flange at landing by a method of rolling stamping (SHO) is resulted. Based on the constructed model, it is possible to model the accumulation of damage by changing the values of the model parameters for different materials and deformation paths, which, in turn, depend on the relative geometric parameters of the workpiece and its location relative to the rolling roll.
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