and Computational Methods

doi: 10.18698/2309-3684-2021-3-323

This paper presents the mathematical formulation and the results of calculations of the problem of metal deformation on a casting-forging module with modified side strikers’ drive. A complex spatial problem of determination the stress-strain state of the flow region under loading with an external load that changes over time is considered. The fundamental equations are based on flow theory. At solving the problem, a proven numerical method is used, as well as numerical schemes and the software package used earlier at solving similar problems. The software package implements a step-by-step loading algorithm considering the history of the process and the changing geometry of the flow region. A small time step is associated with a 10° rotation of the eccentric shaft. The deformation area is divided into elements by an orthogonal system of surfaces (elements have an orthogonal shape). For each element, the formulated system of equations is written in a difference form, which is solved according to the developed numerical schemes and algorithms, that consider the initial and boundary conditions. The result of the solution is the fields of stresses and velocities of displacements in the spatial area. The analysis of the obtained results is given. A comparison with the results of the current structure module solving has been made. Lead is taken as a deformed material, the physical properties of which are approximated by an analytical dependence according to the available experimental data. The physical nonlinearity of the system of equations is realized during solving by the iterative method. Local calculations of the solution of the problem were carried out on three variants of division of the area into elements. The choice of the mesh density imposed on the considered deformation region is substantiated. The solution results are presented graphically. The efficiency of the deformation process according to the improved method on a new design of the casting and forging module is shown.

Одиноков В.И., Дмитриев Э.А., Евстигнеев А.И., Потянихин Д.А., Квашнин А.Е. Математическое моделирование процесса деформации металла на литейно-ковочном модуле с измененным приводом боковых бойков. Математическое моделирование и численные методы, 2021, № 3, с. 3–23.

doi: 10.18698/2309-3684-2023-3-1841

Experimental studies of the flow of liquid metal in the UNRS crystallizer are a long, complex and time-consuming process. Therefore, mathematical modeling by numerical methods is increasingly used for this purpose. A new technology for pouring liquid metal into a crystallizer is proposed. The original patented design of the device, consisting of a direct-flow and rotating gluhodon glasses, is given. The main results of studies of the melt flow in the crystallizer volume are presented. The objects of research were the hydrodynamic and thermal fluxes of liquid metal of a new process of casting steel into a rectangular section mold of the UNRS, and the result was a spatial mathematical model describing the fluxes and temperatures of liquid metal in the mold. To model the processes occurring during the flow of metal in the crystallizer, a specially created software package was used. The theoretical calculations are based on the fundamental equations of hydrodynamics, the equations of mathematical physics (the equation of thermal conductivity taking into account mass transfer) and a proven numerical method. The studied area was divided into elements of finite dimensions, for each element the resulting system of equations was written in a difference form. The result of the solution is the fields of velocities and temperatures of the metal current in the volume of the mold. According to the developed numerical schemes and algorithms, a calculation program has been compiled. An example of calculating the casting of steel into a mold of rectangular cross-section, flow diagrams of liquid metal along various sections of the mold is given. Vector flows of liquid metal in different sections of the mold at different numbers of revolutions of the jacket with vertical ribs are clearly presented. Areas of different turbulence have been identified. The mixing mode at n = 30 rpm is considered optimal. At n = 50 rpm, liquid metal is ejected into the slag bath.

Одиноков В.И., Евстигнеев А.И., Дмитриев Э.А., Карпенко В.А. Математическое моделирование процесса перемешивания жидкого металла в кристаллизаторе установке непрерывной разливки стали. Математическое моделирование и численные методы, 2023, № 3, с. 18–41.

doi: 10.18698/2309-3684-2022-2-6377

The paper presents a mathematical statement and presents the results of calculations in the problem of determining the temperature field during deformation of a strip made of aluminum alloy AD0 on a vertical-type casting and forging module of a new modification. The design of the casting and forging module assumes that one of the four walls of the mold is stationary, the second performs a rotational movement on eccentric shafts, the other two move in a vertical plane, ensuring that the deformed billet is fed down. When solving the problem, a proven numerical method is used. For a moving medium, the heat equation is written in finite difference form in a curvilinear orthogonal coordinate system. The solution of the problem is carried out by the iterative method. When calculating the initial temperature field and its further change, the heat removal on the contact surfaces of the metal with the deformation tools is taken into account. The result of the solution is the temperature field in the spatial domain for discrete times corresponding to the steps of the numerical calculation. At each step, the boundary of the liquid and solidified metal is determined

Дмитриев Э.А., Потянихин Д.А., Одиноков В.И., Евстигнеев А.И., Квашин А.Е. Моделирование поля температур при получении металлоизделий на литейно-ковочном модуле с односторонним воздействием бокового бойка и неподвижной плитой. Математическое моделирование и численные методы, 2022, № 2, с. 65–79