Estimation of heat conduction losses in laser cutting

TLDR: In this article, a mathematical model that is used to estimate heat conduction losses in laser cutting by employing integral methods to solve the three-dimensional, heat-conduction equation is presented.

Abstract: Numerical models of laser cutting are essential for an improved understanding of the process. In order for the models to closely represent real physics the heat lost by conduction during cutting has to be incorporated into them. This paper outlines the details of a mathematical model that is used to estimate heat conduction losses in laser cutting by employing integral methods to solve the three-dimensional, heat-conduction equation. Simple, yet accurate, correlations are presented for the conduction heat loss rate, as well as for characteristic thicknesses of the heat affected zone (HAZ). These variables are functions only of Peclet number (Pe), which may be thought of as a dimensionless cutting speed. The correlations are then used to predict (i) the cutting speed in laser cutting, and (ii) the temperature field in the HAZ. The predictions show an excellent match with experimental results. Cutting speed is predicted using an energy balance at the cutting front. An implicit, nonlinear equation for Pe as a function of Stefan number (Ste) and dimensionless heat of combustion results. Ste gives the ratio of sensible heat to latent heat in the workpiece. Detailed analysis of beam absorptivity, coupled with the dimensionless cutting speed result suggests that the dimensional cutting speed, uo, may be correlated as a unique function of the ratio of incoming laser power to workpiece thickness, Qlas/d. This is corroborated by measured cutting rates over a wide range of sample thicknesses and two beam power settings.