Analytical solution for three-dimensional model predicting temperature in the welding cavity of electron beam

This paper provides an analytical solution for three-dimensional model predicting temperature in the welding cavity of electron beam. It is not easy to measure the temperature on the keyhole of electron-beam welding. Therefore it is essential to develop an analytical model that can accurately predict the temperature in the keyhole. In this study, the keyhole produced by an electron beam is assumed to be a paraboloid of revolution and the intensity of electron beam is supposed to be Gaussian profile. In order to obtain an analytical solution, the parabolic coordinate system is utilized to analyze the temperature in the keyhole and the parameter approximating convection is proposed to account for the effect of convection of molten metal. Considering the momentum balance at the bottom of the keyhole but neglecting the absorption in the plume, an analytical solution is developed for semi-infinite workpieces. As compared with other analytical solutions, the analytical solution obtained by this model provides the temperature distribution more consistent with the experimental data. The effects of various parameters on the temperature distribution in the keyhole are also discussed in this study.