Mathematical modeling in cold extrusion processes by using kinematic modules of complex configuration

Abstract

Grudkina N. S. Mathematical modeling in cold extrusion processes by using kinematic modules of complex configuration. Material working by pressure. 2020. № 1 (50). Р. 45-49.

The calculation of the relative pressure value inside the trapezoidal axial kinematic module by using energy upper bound method is considered. The sloped boundary of this module is reflected the features of the against punch configuration (angle of slope). To simplify the power of deformation forces in the area of the developed trapezoidal module is used upper bound theory with Cauchy-Bunyakovsky. To calculate the value of the relative pressure power of deformation forces inside the axial module, power of friction forces on the billet contact surface, against punch and shearing forces with adjacent kinematic modules are determined. Thus, it is possible to study the influence of the slope angle in against punch on inclination of the relative pressure value and to consider it as an optimization parameter. The influence of different friction conditions and flange zone thickness on inclination of the relative pressure value in deformation are determined. The nature of the theoretically obtained curves from relative pressure value in high values of the flange zone thickness and disregarding friction on against punch surface differs from other ratios by the absence of a minimum point are obtained. Under these conditions, the axial trapezoidal kinematic module is degenerated into a triangular with preserving previously received calculations. For other process ratios, optimal values are determined that represent the angle of against punch inclination that indicates the possibility of optimizing the relative pressure value. Thus, the possibility of determining the optimal configuration in the lower tool is confirmed. The obtained results in simulating of cold extrusion processes with a transition from forward to radial flow, which will recommend for defining the optimal configuration in the tool and development of appropriate design solutions are determined.