Using the calculation schemes CS-1 (with the presence of a trapezoid module) and CS-1a (with rectangular kinematic modules) has been proposed for the process of the combined radial-direct extrusion of parts with a flange and an axial protrusion. The application of a trapezoidal kinematic module allows the description of the characteristic regions of metal flow, close to the actual course of the process based on the distorted coordinate grids. On the basis of the energy method, the values of the reduced deformation pressure have been obtained using the upper estimate of the power of deformation forces inside the trapezoidal kinematic module. The optimization involved the parameter Rk that determines the position of the surface of the interface of metal flow into an axial protrusion and a flange zone. We have performed a comparative analysis of the theoretical calculations of the magnitude of the reduced deformation pressure and the influence of geometric ratios and friction conditions on the qualitative and quantitative differences in the character of the change in the resulting curves. The overestimation of data on assessing the force mode based on the CS-1a scheme relative to the calculations based on the CS-1 scheme can be as high as 50 % and indicates the rationality of using the latter. This is due to the limitation in the use of the optimization (the absence of the optimization of the height of the deformation site) for the scheme containing elementary rectangular kinematic modules. The deviation from the experimentally obtained increments in an axial protrusion does not exceed 7-10 %, which indicates the validity of the use of the CS-1 estimation scheme with a trape zoidal kinematic module. Thus, it can be argued that it is correct to determine the position of the boundary of the surface of the interface of metal flow into an axial protrusion and a flange zone and the resulting assessment of the formation of a semi-finished product
The article is considered a comparative analysis for predicting defect such as dimple by energy method of power balance, upper bound method and finite element method. The upper bound method takes into account the geometrical position and dimension of the dimple, the criterion for the formation in dimple by energy method of power balance is the presence of a minimum point in the function of relative pressure on the relative velocity of metal outflow in the vertical direction. New engineering calculations for the relative pressure are developed in combined radialbackward extrusion process by using a kinematic module with fillet. A comparative analysis of the obtained data has been carried out by energy method of power balance, upper bound method, computer simulation by Qform 2/3D program and experimental data. Rationality of using the energy method of power balance in view of its efficiency and the possibility of taking into account various friction conditions and the presence of fillet on the matrix, as well as smaller deviations from the results of finite element simulation and experimental data have been defined. Providing more conditions that are favorable for friction in the bottom of the billet and in the flange area in comparison with the friction conditions on the glass wall contribute to delay in the dimple appearance. It was found that the radius of fillet makes it possible to delay the dimple appearance by the approximately (0,4 ÷ 0.5R) mm for the entered radius of fillet R. This allows us to expand the possibilities of obtaining parts with a flange by combined radial-backward extrusion without the formation of a defect such as dimple.