Abstract
Оn the basis of the variational method, a mathematical model has been developed and calculations of energy-power parameters of the process of stamping the heads of rod fasteners with a flange have been performed. The relations of the deformation theory of plasticity were used. The rheological properties of the deformable metal were set as a model of a rigid-plastic medium with nonlinear hardening. The hardening curve was described by an exponential dependence proposed by G. A. Smirnov-Alyaev. The stamping process was considered in a cylindrical system of coordinate axes r, z, 
. The volume of the head was divided into rigid and plastic regions, the interface between which was described by a quadratic parabola with a variable parameter a. The plastic area was divided into two zones. For each zone were asked the functions of the radial displacements 
, that are consistent with the boundary conditions and was very close to the actual metal flow. Using the corresponding Cauchy differential dependencies and the incompressibility condition, the components of the strain tensor 
and the strain intensity 
, were determined, using which the work of internal forces, friction forces, and shear forces was determined. The search for the minimum of complete deformation operation A min was performed by numerical methods using a specially developed program. According to the found values of the minimum total deformation work A min the stamping forces P and the specific forces 
, where 
is the cross-sectional area of the rod, were determined. Based on the results of calculations, a nomogram was constructed that allows determining the specific forces p of stamping depending on the relative dimensions of the head flange for rod fasteners made of 10, 20Г2P, 30Г2P, 30ХР and 40X steels. Experimental studies were carried out, during which heads with a flange were stamped out of grade 10 steel. The discrepancy between theoretical and experimental results was 5.7 %.
Keywords
Rod fasteners, head with flange, variation method, displacement functions, work of internal forces, work of friction forces, power parameters, stamping forces.