Reconstruction of the Thermal Source from the Temperature Measured Case of Surface Heat Treatment of Steel by Laser Beam

The problem posed in the surface heat treatment industry of metallic materials is the knowledge of the amount of energy required and its correct distribution on the treated surface for the achievement of a better quality of the metallurgical structure of treated parts. To succeed in this operation, manufacturers are required to carry out many expensive and time-consuming experiments. This work consists in predicting the energy density applied to the surface of a metal part, during surface heat treatment by a laser beam, based solely on temperature measurements taken under the treated surface. This problem in the mathematical sense is called the reverse heat transfer problem. The solution of this inverse problem of heat conduction allows us to predict the density of the energy necessary to be applied to the surface from the desired metallurgic structure characterized by a well-defined temperature distribution. The optimization method used in this work is that of the conjugate gradient thanks to its speed of convergence, its quality of precision and also to stability. Many similar works have been developed in the literature using the inverse method but only to estimate thermo-physical characteristics such as thermal conductivity, thermal capacity mass, point heat source, etc. using conventional numerical methods. But in no case to estimate the complex profile of an energy density applied to the real processing of steel using the conjugate gradient algorithm.