Tool profile stationarity while simulating surface plastic deformation by rolling as a process of flat periodically reproducible deformation

OBRABOTKAMETALLOV MATERIAL SCIENCE Том 20 № 3 2018 EQUIPMEN . INSTRUM TS Vol. 3 No. 2 2021 [9-10]. Improper process parameters lead to the fact that the increase in fatigue strength and the surface roughness reduction is slight, and, in some cases, can lead to surface condition deterioration [11–13]. The problem of determining the surface layer properties during deep rolling is complex due to the properties final values are determined not only by the finishing parameters, but also by the history of the surface layer metal loading during previous processing operations [14-15]. This phenomenon is called technological inheritance. There are a large number of works aimed to predict the processing result by simulation the deep rolling process nowadays, in this case, direct processing parameters or determined processing parameters (for example, contact pressure) can be used as initial data for simulation [16–19]. One of the promising approaches to the design of hardening technological processes by rolling, taking into account the loading history, is the mechanics of technological inheritance [20]. The main parameters of the surface layer state are the shear strain degree L , which characterize the surface layer hardening, the plasticity reserve exhaustion degree Y , which characterize the accumulated damage of the surface layer metal, and the residual stress tensor, in accordance with the key provisions of the technological inheritance mechanics. The calculation of the stress and strain values required calculating the values of the accumulated degree of shear deformation and the degree of depletion of the plasticity reserve is possible by finite element simulation of the volumetric stress-strain state during contact interaction of the roller and the part. However, the nonlinear nature of this problem, the need to use elements of small size, which leads to a large number of it, leads to a significant increase in the complexity of creating a model and the calculation time. Therefore, the possibility of finite element simulation of the contact interaction of the roller and the workpiece in a flat setting is important. It is shown in [21] that deformations in the tangential section of the workpiece (in the plane perpendicular to the sample axis) are small compared to the deformations in the axial section (in the plane on which the axis of the workpiece lies). This makes it possible to calculate the stress-strain state during rolling in a plane-deformed formulation, considering it as a process of plane fractional deformation. In this case, the displacement of material particles, the occurrence and change of stresses and deformations are considered in the plane of deformation (axial section of the part) when it rotates about the axis of the part during processing. The roller profile at each time is defined as the intersection line of the roller surface and the strain plane. Obviously, the roller profile will change when the rotation angle of the strain plane changes. In this regard, an important issue that determines the possibility of the rolling simulation as a plane-stain process using a constant profile roller model is the assessment of the change magnitude in the roller profile when the strain plane is rotated. The work purpose is to estimate the change magnitude in the roller profile in the strain plane while rolling when this plane is rotated. The work tasks are analytical description of the tool profile in the strain plane depending on the rotation angle of the strain plane of deformation, determination of the lines points coordinates of the tool profile when the strain plane is rotated, and determination of the relative change in the points coordinates of the roller profile when the strain plane is rotated. Methods In the process of rolling in the contact zone of the tool with the part, a deformation zone occurs – a local region of plastic deformation. A characteristic feature of the deformation zone in the part axial section of the part is the presence of a plastic wave in front of the roller. At each part turn, the roller is shifted relative to the deformation zone formed on the previous turn by the feed amount. On the other hand, under the roller immobility assumption, each material point of the part moves in a spiral, shifting in the axial direction relative to the roller by the feed amount for each part turn. The trajectories of material particle movement in the deformation zone are called flow lines . When a material