Vibrations in engineering and technology

Sivak Roman - Doctor of Technical Sciences, Associate Professor of the Department of General Technical Disciplines and Labor Protection of Vinnytsia National Agrarian University (3 Sonyachna St., Vinnytsia, Ukraine, 21008, e-mail: sivak_r_i@ukr.net) 

Нunko Iryna - Candidate of Technical Sciences, Associate Professor of the Department of General Technical Disciplines and Labor Protection of Vinnytsia National Agrarian University (3 Sonyachna St., Vinnytsia, 21008, Ukraine, e-mail: irynagunko@vsau.vin.ua). 

Zalizniak Roman - graduate student of the Department of General Technical Disciplines and Labor Protection of Vinnytsia National Agrarian University (3 Sonyachna St., Vinnytsia, Ukraine, 21008, e-mail: pacifistroma@gmail.com)  

Methods of theoretical solution of problems in the processing of metals by pressure are insufficiently developed for practical use in the development and implementation of new technologies and improvement of existing ones. To meet the stringent requirements for the accuracy of determining the stress-strain state, it is necessary to have reliable information about the evolution of the development of the plastic deformation process at each point of the metal from the very beginning of the deformation. This will allow to obtain with high accuracy the important characteristics of the technological heredity of the products that they acquire as a result of their plastic processing. The first and important step in the calculations of the stress-strain state is to obtain the kinematic characteristics of the plastic flow of metal in the form of analytical dependences, which will formulate the patterns of deformation in the technological processes of metal forming.

The article considers the possibility of applying the method of current functions to determine the components of the strain rate tensor in established stationary processes of plastic deformation. It is assumed that in the case of axisymmetric plastic deformation of a metal in a channel with curvilinear boundaries, the kinematics of the process is similar to a plane flow. In obtaining the equations, the differential equation of current lines taking into account the incompressibility condition was used to determine the components of the strain rate tensor. To explain the physical meaning of the current functions, two infinitely close current lines were considered in the flow plane, and an expression was obtained for the flow through a finite transverse current tube. In the absence of radial velocity components at the boundaries, constraints are obtained that are imposed on derivatives of current functions at these boundaries. The developed method of calculating the kinematic characteristics of plastic deformation for established axisymmetric stationary processes will simplify the mathematical processing of the obtained results and increase the reliability of the determination of the stress-strain state.

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