Point and line sources: models of power absorption in the theory of welding

Abstract

Rosenthal’s point source and line source solutions are two very simple exact solutions of the equation of heat conduction. They give the temperature field in the work piece when the source of power is in steady relative motion and a steady state has been achieved; they have been very influential in the development of useful theoretical models of welding. They have their limitations however; a particularly obvious example in the context of the use of lasers for welding is the failure of the line source to describe the “nail-head” shape of the cross section of the fusion zone in the case of the keyhole weld. Steen suggested that a superposition of a point and a line source might provide a more satisfactory description of a keyhole weld. The idea proved to be extremely successful and has led to numerous adaptations and elaborations of the idea, some of which are reviewed in this paper.Rosenthal’s point source and line source solutions are two very simple exact solutions of the equation of heat conduction. They give the temperature field in the work piece when the source of power is in steady relative motion and a steady state has been achieved; they have been very influential in the development of useful theoretical models of welding. They have their limitations however; a particularly obvious example in the context of the use of lasers for welding is the failure of the line source to describe the “nail-head” shape of the cross section of the fusion zone in the case of the keyhole weld. Steen suggested that a superposition of a point and a line source might provide a more satisfactory description of a keyhole weld. The idea proved to be extremely successful and has led to numerous adaptations and elaborations of the idea, some of which are reviewed in this paper.