Analysis of Characteristic Values in Laser Beam Processes with a Gaussian Distributed Heat Source

Moving heat sources, from lasers to welding arcs, are often represented as radially symmetrical Gaussian distributions of heat fl ux. This problem has a known closed-form solution; however, despite its relevance and apparent simplicity, the solution is not used in industrial (and most research) settings. One of the obstacles to the implementation in practice of the known solution is that it involves an improper integral and has the form of temperature as a function of spatial position. Numerical operation involved in the implementation is simple for an expert but out of reach for a practitioner in industry. An additional challenge for practitioners is that a Gaussian moving heat sources involves a large number of parameters, making it difficult to intuitively grasp the problem. This presentation will discuss the application of dimensional analysis to simplify the problem to the minimum number of dimensionless groups. Asymptotic analysis of the exact solution to express characteristic values of a welding pool (such as maximum temperature, heating rate and temperature gradient) will be introduced. Churchill’s blending functions will be applied to obtain general and simple equations with accuracy higher than can be discriminated experimentally. Machine operation and expensive material costs will be significantly reduced by predicting important parameters from theory rather than “trial and error” approach. A comparison with previous applications of dimensional analysis to this problem, the extension (and challenges) of this methodology and one specific example will also be discussed.