The use of TFBGF method with a 3D transient analytical solution to solve an inverse heat conduction problem in the presence of a moving heat source

Abstract

Moving heat source are present in numerous problem pratical in ingeenring. For example, machining process as the Gas tungsten arc welding (GTAW) , laser welding, friction stirwleing process or milding problem. Moving heat source are also present in biological heating as the metabolism or in heat thermal treatment. All this case, the heat input identification is a complex task and represents an important factor in the optimization of the process. The aim of this work is to investigate both the temperature field as the heat flux delivered to a piece during a process with moving heat source. The temperature measurements are obtained using thermocouples at accessible regions of the workpiece surface while the theoretical temperatures are calculated from a 3D transient heat conduction thermal model with a moving heat source. The thermal model solution is obtained analytically (direct problem). The inverse problem, it means, the estimation of the moving heat source, uses the Transfer Function Based on Green’s Function (TFBGF) method. This method is based on Green’s function and in the equivalence between thermal and dynamic systems. The technique is a simple approach without iterative processes, and therefore extremely fast. From the knowledge of both the temperature profile (hypothetical or experimental temperature far from the heat source) and of the transfer function it is possible to estimate the heat flux by an inverse procedure of the Fast Fourier Transform (IFFT) . The TFBGF is, then, adapted to solve an inverse heat conduction problem with a moving heat source. Simulated and experimental test are used for estimating the heat source delivered to the piece. The estimation of the moving heat source without use of minimization least square, or optimization technique is the great advantages of the technique proposed here. The moving heat source can, then, be obtained directly from the temperature measured since the 3D transient analytical solution is obtained and the TFBGF can be applied in that solution.