CW laser machining of hard ceramics—I. Effects of three-dimensional conduction, variable properties and various laser parameters

Abstract

A three-dimensional conduction model has been developed to predict the temperature distribution inside the solid and the shape of a groove formed by partial evaporation of a semi-infinite body using a moving CW laser with a Gaussian beam profile. This has application in laser machining where material is removed by repeated scanning of a focussed beam on the workpiece surface. The governing equations are solved using a finite-difference method on an algebraically-generated boundary-fitted coordinate system. The groove shape and temperature distribution in the solid for both constant properties and variable properties, for different speeds, for various laser power levels and for different beam profiles are presented. The groove shapes for constant thermal properties are compared with a previous three-dimensional boundary element conduction model solution and a quasi-one-dimensional conduction model solution, in which the conduction losses were approximated using a simple integral method. The present model compares well with the three-dimensional boundary element model for all ranges of laser parameters, and, when thermal losses due to conduction are minor, the one-dimensional results are also in good agreement. Experimental results were obtained for material removal rates and groove shapes on silicon nitride, which were found to agree well with theoretical predictions for shallow grooves. For deeper grooves in silicon nitride beam guiding (i.e. multiple reflections within the groove) comes into play and the assumptions in the model are violated.