The development of triangular kinematic module to calculate the deformation pressure in the extrusion processes

Abstract

Аliieva L. І., Levchenko V. M., Aliiev I. S., Kartamyshev D. O. The development of triangular kinematic module to calculate the deformation pressure in the extrusion processes
 The article presents the universal kinematic module developed on the basis of the energy upper bound method, designed for use in mathematical simulations of combined processes of cold forging. In particular, this module can be used for force regime simulating and tool loads analyzing at radial-forward extrusion of hollow products with blind hole of continuous workpieces to describe deformation zones during metal flow to the center and turn zones from radial flow to backward one. The kinematically possible velocity field for convex curvilinear (parabolic) triangular module and the equations of its parabolic inclined boundary are given. Analytical dependencies for power of deformation forces, friction and shear at the boundaries of the module, as well as for the reduced pressure in a parametric form are obtained. The developed curvilinear kinematic module, the use of which makes it possible to increase the efficiency of the upper bound method for studying the processes of combined extrusion, has been tested and described. It is shown that value of reduced pressure for the curvilinear turn module is most affected by the relative thickness of the flange, its radius, the thickness of the wall of the tubular workpiece, as well as friction conditions. The possibility of correct using of curvilinear triangular module for the analysis of complex schemes of processes with several zones is demonstrated. The simulation for calculation schemes of radial-forward workpiece extrusion with variable flange height was carried out. It has been determined that the developed curvilinear triangular module due to the reducing the value of the velocity jump at its boundaries, makes it possible to reduce the upper estimate of the tool loads in comparison with the variants of simulations that were previously based on rectangular modules.