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A computer model has been developed to investigate the processes of heat and mass transfer under the influence of concentrated energy sources on materials with specified thermophysical characteristics, including temperature-dependent ones. The model is based on the application of the volume of fluid (VOF) method and finite-difference approximation of the Navier–Stokes differential equations formulated for a viscous incompressible medium. The “predictor-corrector” method has been used for the coordinated determination of the pressure field which corresponds to the continuity condition and the velocity field. The modeling technique of the free liquid surface and boundary conditions has been described. The method of calculating surface tension forces and vapor recoil pressure has been presented. The algorithm structure is given, the individual modules of which are currently implemented in the Microsoft Visual Studio environment. The model can be applied for studying the metal transfer during the deposition processes, including the processes with electron beam spatial oscillation. The model was validated by comparing the results of computational experiments and images obtained by a high-speed camera.

The mathematical formulation of electron beam melting and liquid metal transfer model in wire-based additive manufacturing with temperature dependencies of thermophysical properties is described. A description of the model algorithmic implementation based on the use of numerical methods for solving the Navier-Stokes equations system and the Volume of Fluid (VOF) method for tracking the free surface of a liquid on the cubic mesh cells is given. An iterative method for calculating the pressure field that ensures the fulfillment of the incompressibility condition for a viscous fluid is described. The paper also paid attention to the description of methodology for calculating the forces acting on the free surface of the melt, including surface tension forces and metal vapor pressure forces. One of the key elements of the proposed model is method for volumetric distribution of electron losses calculating, considering their scattering during the interaction of an electron beam with a curved melt surface. Electron beam focusing influence on the distribution of energy losses and the dynamics of penetration channel formation has been studied. An algorithm for visualizing the free surface of the melt based on the use of the Gaussian function, is described.

The energy spectra of the ion saturation current of the Langmuir probe in the plasma formed over the keyhole directly during the process of electron-beam welding of steel 09G2S with the varied parameters (e.g., the welding speed and focus coil current) has been investigated. The presence of typical zones with the energy spectrum peaks in the low-frequency and high- frequency bands has been shown. It has been established that the peak location in the high- frequency range of the energy spectrum does not depend on the welding modes and the position of the probes relative to the keyhole. The low-frequency range of the energy spectrum depends on the vapor flow density of the keyhole and is rather sensitive to the welding modes. The use of electron beam oscillation makes it possible to control plasma flows and hydrodynamic processes in the penetration channel.

Molten pool free surface shape calculation and its evaluation in time for analysis of electron beam melting and welding processes is a very important problem. Unfortunately, experimental methods can provide only a part of the necessary information. Electron beam heating creates the conditions for intense metal transfer, and pool surface shape affects the energy absorption efficiency. This paper reports the method which combines the Monte-Carlo simulation for spatial and energy parameters of heating source calculating with the Volume of Fluid algorithm for liquid free-surface numerical evaluation. The velocity and pressure field technique calculation in a molten pool with the action of surface tension forces and vapor recoil pressure is described. It is shown that the proposed simulation method allows to study heat and mass transfer transient processes, including deep penetration channel formation. Model validation was carried out. Simulation results are shown to be consistent with experimental data obtained using a high-speed camera.

Existing analytical methods for calculating electron-beam welding modes, which provide welds with required penetration depth, are described, and main disadvantages of these methods are shown. A new calculation method based on a model of moving cylindrical heat source, which involves moving of a cylinder with constant surface temperature in an infinite plate, is proposed. The proposed calculation method takes into account energy losses during metal melting and its partial evaporation. A comparison of experimental and calculated data obtained using the developed method and existing methods, is presented. Plates with a thickness of 32 mm from 5V titanium alloy, 27 mm from 40 Kh13 steel and 20 mm from D16 duralumin were used for experiments. It was shown that the developed method application made it possible to calculate with appropriate accuracy a required beam power during EBW of various materials.

The paper is devoted to the study of the thermo-EMF of various metals and alloys, which are widely used in welded structures. For the selected steels, the relationship between the absolute thermo-EMF and their structural class was established, and the dependences of the thermo-EMF on temperature were obtained. For some groups of steels, a method of predicting the thermo-EMF by chemical composition was developed.

The work describes a method for measuring the magnetic field induced by thermoelectric currents in control points above welded specimens and presents the measurement results. The dissimilar 60-mm thick steel samples are welded by electron-beam welding (EBW). The grades of the pairs of steels are 09Mn2Si + 12Cr18Ni10Ti, 09Mn2Si + 20Cr13 and 20Cr13 + 12Cr18Ni10Ti. The study shows that the electron beam in the weld root deflects towards the material with larger positive potential of integral thermal EMF. The deflection is uneven along the specimens, which necessitates taking into account the geometry of welding joints when elaborating the mathematical models of the process. Maximum deflection for the studied pairs of materials correspondingly amounts to 0.6, 2,8 and 3.8 mm, which is critical for producing a high-quality seam. In addition, the alteration of magnetic induction in control points during EBW was obtained.

Annotation The paper derives a relation describing the shape of an electron beam axis affected by thermoelectric currents during welding of dissimilar materials. The treatise suggests a new method for determining the adjustment actions for preventing lack of penetration in the weld root and derives an expression for determining the critical degree of weld penetration during welding of dissimilar austenitic and pearlitic steels. The received results can be used to make high-quality welding connections of thick dissimilar materials by eliminating incomplete penetration and ensuring necessary penetration degree of welded edges along the whole part thickness.

The paper is devoted to the definition of the minimum electron beam power that is required to obtain stable layer formations during the additive electron beam wire deposition. Correlation between the minimum energy that is needed for stable deposition and the deposition speed has been established. Additionally, the influence of the electron beam oscillation type on geometrical parameters of single layers have been investigated.

The paper is devoted to the study of welded joints formation process both from homogeneous and dissimilar materials. The investigated welded joints were made by an electron beam using intermediate inserts of small thickness in a narrow gap. The influence of insert size as well as gap size on the stability of weld formation is shown. Electron beam oscillation configurations which eliminate incomplete penetration in weld root are determined. Values of thermal efficiency are experimentally found for different welding speeds. The results of structure study for dissimilar welded joints of plates from carbon steel 20 and austenitic corrosion-resistant AISI 316L steel are presented. The values of penetration rate for base and filler metal are calculated and experimentally confirmed.