Development of calculation schemes for the combined extrusion to predict the shape formation of axisymmetric parts with a flange

Derivation of engineering formulas in order to calculate energy-power parameters and a shape change in a semi-finished product in the process of combined extrusion

“…An analysis of data from the scientific literature reveals that the main problem of studying the processes of combined extrusion with several degrees of metal flow is to determine the optimal kinematic parameters of the deformation process [6][7][8][9][10][11][12][13]. This, in turn, makes it difficult to obtain the information about the stagewise and limit change in the shape of a billet [6] and leads to complexities in the development of the technological mode.…”

“…Thus, it is difficult to predict a stagewise change in a shape of a billet. In paper [12], the process of the combined radial-reverse extrusion with a disjointed and joined deformation site was explored and the limits of using the proposed computational schemes were established. In addition, for the schemes with an axial trapezoidal module with a sloped curvilinear boundary of flow separation, the magnitudes of increments of a semi-finished product and reduced pressure in the explicit form were not obtained.…”

“…Therefore, this method for simplification of integrand expressions to calculate the power of deformation forces is ineffective. The intensity of deformation rates  ε i for the kinematic module in its original form for the rectilinear border enabled us to find the power of deformation forces and the magnitude of reduced pressure p 1 in the analytical form [12].…”

“…< Calculation formulas for determining the magnitude of reduced pressure and increment in dimensions of a semi-finished product were obtained [12]. The use of a curvilinear sloped border in the form T = T 3 (z) in modeling process of the combined radial-reverse extrusion of parts with a flange showed the effectiveness of using at 2 1…”

“…Determining the boundaries of using the proposed calculation schemes with the possibility to obtain the data on a change in the shape of a semi-finished product in the form of ready formulas is an urgent task in this case. Based on the ease of comparing the obtained engineering formulas p 1 [12] and the proposed formula p 2 , condition of the preferable use of the calculation scheme with T = T 2 (z) takes the form p p 2 1 < . Thus, admission  γ r z = 0 is correct and the given kinematic module with a curvilinear boundary in the form of T = T 2 (z) can be recommended for the use in the framework of the calculation scheme of the combined radial-reverse extrusion.…”