Investigating the Process of Shrinkage Depression Formation at the Combined Radial-backward Extrusion of Parts with a Flange

The possibilities of using an energy method to forecast defect formation in the form of shrinkage depression in the combined extrusion processes have been investigated. We have proposed a mathematical model of the combined radial-reverse extrusion process of hollow details with a flange, taking into consideration the degeneration of the trapezoidal module into a rectangular one. Separate stages in the deformation process have been defined, depending on the magnitude of the active tool stroke compared with the thickness of the bottom of the cup. We have devised a generalized estimation scheme for the process of combined radial-reverse extrusion of parts with a flange taking into consideration the final stage of deformation (Hbottom<h1). The magnitude of the reduced pressure of deformation has been derived as a function of the geometric, technological, and kinematic parameters of the extrusion process. A role of the kinematic parameter of the process belongs to a relative speed of metal flow in the vertical direction (filling the cup's wall at the inverse flow of metal). The magnitude for the reduced pressure of deformation has been optimized based on this parameter. We have analyzed the character of change in the optimum magnitude of a relative speed of metal flow in the vertical direction in the course of the process. The differences have been established in the derived dependences of a given kinematic parameter for the process with the formation of shrinkage depression in the bottom part of a component and without defect formation.It has been substantiated that the use of combined extrusion in the manufacture of hollow parts with a flange, when compared with the application of simple schemes of deformation, improves the technological capabilities of the process. We have proven that the technologies for introducing combined extrusion had not been sufficiently studied and there is a lack of recommendations on predicting the formation of a defect in the form of shrinkage depression. The estimation scheme has been proposed for the radial-reverse extrusion process, taking into consideration the emergence of shrinkage depression at the final stage of deformation. We have modeled the process of combined extrusion of hollow parts with a flange and established the influence of friction conditions on the time of the emergence of shrinkage depression in the bottom part of a component.It has been confirmed that the proposed generalized estimation scheme makes it possible to predicting the occurrence of a defect in the form of shrinkage depression at all stages and under different technological conditions for a deformation process. Obtaining a preliminary assessment, based on it, of possible defect formation would facilitate the development of appropriate technological recommendations to avoid defects of this typ

Designing A Kinematic Module with Rounding to Model the Processes of Combined Radial-longitudinal Extrusion Involving A Tool Whose Configuration is Complex

It is advisable that parts whose shape is complex and which are made from solid or hollow blanks should be made by means of transverse and combined radial-longitudinal extrusion. The variation of manufacturing modes, tool configurations (in the form of chambers and rounding of the transitional sections of matrices) requires an adequate preliminary assessment of the force regime and the features of part shape formation. This paper has proposed a curvilinear kinematic module of the trapezoidal form for modeling radial-longitudinal extrusion processes in the presence of matrix rounding. Given the impossibility of using a quarter-circle boundary for the kinematically assigned possible velocity field, it has been proposed to use approximate curves in the form of z1(r) and z2(r). Taking into account the slightest deviation in the length of the arc of the approximate curve z1(r) and the area of the curvilinear trapezoid bounded by it relative to a quarter of the circle (not exceeding 0.8 % for any ratio), it has been recommended using this particular replacement. We have performed calculations of the value of the reduced deformation pressure inside the kinematic module with rounding taking into consideration the power of cutting forces at the border with adjacent kinematic modules. As an example, the devised module with rounding embedded in the estimation scheme of radial extrusion was analyzed. A significant impact of friction conditions on the force mode and the corresponding optimal value of the rounding radius have been identified. The resulting kinematic module makes it possible to expand the capabilities of the energy method for modeling cold extrusion processes involving the tools of complex form according to new deformation schemes. That could contribute to preparing recommendations on the optimal tool configuration and more active industrial implementation of these processe

Predicting the Shape Formation of Parts with A Flange and an Axial Protrusion in the Process of Combined Aligned Radial-direct Extrusion

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 trapezoidal 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 produc