Mathematical Modeling of Energy Distribution in Entering a Beam into the Workpiece Material in the Course of Electron Beam Welding

Modeling of electron beam welding processes is one of the most important parts of applied research, because full-scale experimental investigations are either expensive or highly labor intensive. The problem of modeling the temperature fields at the electron beam entering stage during welding is considered. The aim of the study is to simplify the adjustment of the electron beam welding process technological parameters and to elaborate and develop more efficient control algorithms through replacing full-scale experiments by model ones. The mathematical body of the proposed solutions is constructed using the theories of thermal and welding processes, based on which the energy distribution mathematical models are developed. For practically implementing the computations, an algorithmic support is presented that allows the mathematical models to be applied in modern modeling systems, such as Matlab, Comsol Multiphysics, and Ansys. Apart from supplementing the set of existing mathematical models of the electron beam welding process, the obtained models for calculating the temperature in the beam entering area widen their application for calculating and optimizing the welding process, taking into account the workpiece temperature in the electron beam entering area. By using the proposed solutions, several numerical experiments were carried out for a workpiece made of VT-14 titanium alloy and two pieces of different thickness made of AMg-6 aluminum alloy. The obtained temperature fields and the rms values of process parameters are almost identical with the results of previously conducted full-scale studies.