Application of melt pool profiles for parameter calibration of Goldak’s heat source model

Abstract

Goldak’s ellipsoidal heat source model is widely accepted in laser powder bed fusion (LPBF) process simulations. The model is dependent on three inherent flux distribution parameters and absorptivity which need to be calibrated before application. However, the uniqueness of the calibrated heat source parameters has not been established, which is crucial to accurately represent the energy density distribution in numerical studies. This paper proposed a novel parametric optimization method that can uniquely calibrate these four heat source parameters with high accuracy. Both the simulated cross-sectional (CS) profile and the mid-front (MF) profile of the melt pool were used during calibration. The differences between the experimental and simulated profiles formed the objective function of the parametric optimization problem, which was calculated by using the least power norm method on the deviations between melt pool boundary curves. A genetic algorithm (GA) with elitism selection approach was employed to optimize the heat source parameters by minimizing this single objective function value. To theoretically verify the applicability of the method, two theoretical case studies involving two distinct sets of heat source parameters were carried out. A unique solution of Goldak’s heat source parameters with less than 2 % error can be achieved within 50 generations of the optimization process. A single-track experiment was conducted to demonstrate the application of the proposed method in a real scenario. The CS and MF melt pool profiles were extracted and the calibration procedure was applied. The profiles from simulation with the calibrated heat source parameters exhibited a good agreement with experimental results. The calibrated parameters were used to simulate multi-track printing on a single layer for validation of the proposed method. The CS melt pool profiles obtained from the multi-track simulation and multi-track experiment agreed well, which validated the accuracy of the proposed calibration method and its utility in obtaining the key Goldak heat source parameters for LPBF simulation.