Integral equations of deformation of cylindrical workpieces in axisymmetric matrices of complex shape


The article considers the process of deformation of thin-walled pipes using complex-shaped tooling. The article solves the actual problem of elastic and plastic deformation of pipe blanks in the stamping process, taking into account physical nonlinearity since the power law of hardening is taken into account, as well as the compressibility of the material at the stage of elasticity. When determining the stress and strain state during the deformation of thin-walled pipe blanks using axisymmetric tooling, the method of variable elasticity parameters was used, which allows taking into account not only the change in thickness during deformation but also the compressibility and nonlinearity of the hardening of the material. Integral equations are obtained for various processes: crimping and drawing, distribution, and broaching of a pipe billet. The described processes differ in the way the external load is applied. For all processes, two sections with different directions of curvature in the meridional section can be distinguished. The solution for determining the stress and strain state of the pipe, in accordance with the method of variable elasticity parameters, is proposed to be carried out by the method of successive approximations according to the constructed recurrent scheme.