Semi-Analytical Solution of the Thermal Field Induced by a Moving Double-Ellipsoidal Welding Heat Source in a Semi-Infinite Body

Abstract

This paper introduces the solution of the thermal field induced in a semi-infinite body by a moving heat source with Gaussian distribution inside a double-ellipsoidal volume. This heat source model was introduced by Goldak et al. (1984) for the simulation of welding processes. It is the most widely used model nowadays mainly thanks to its versatility to accommodate a wide variety of welding techniques. Two different semi-ellipsoidal volumes are defined corresponding to the front and the rear of the moving source. The analytical solution proposed by Nguyen et al. (1999) is only correct when both semi-ellipsoids are equal, i.e. for Goldak et al.’s (not-double-) ellipsoidal model. The correction needed to extend Nguyen et al.’s analytical solution to the double-ellipsoidal case is presented here.
The same problem is then solved using two- and three-dimensional finite element models, in order to evaluate these models in terms of accuracy and computational cost.