Printed layers height calibration curve and porosity in laser melting deposition of Ti6Al4V combining experiments, mathematical modelling and deep neural network

Purpose Porosity is a commonly analyzed defect in the laser-based additive manufacturing processes owing to the enormous thermal gradient caused by repeated melting and solidification. Currently, the porosity estimation is limited to powder bed fusion. The porosity estimation needs to be explored in the laser melting deposition (LMD) process, particularly analytical models that provide cost- and time-effective solutions compared to finite element analysis. For this purpose, this study aims to formulate two mathematical models for deposited layer dimensions and corresponding porosity in the LMD process. Design/methodology/approach In this study, analytical models have been proposed. Initially, deposited layer dimensions, including layer height, width and depth, were calculated based on the operating parameters. These outputs were introduced in the second model to estimate the part porosity. The models were validated with experimental data for Ti6Al4V depositions on Ti6Al4V substrate. A calibration curve (CC) was also developed for Ti6Al4V material and characterized using X-ray computed tomography. The models were also validated with the experimental results adopted from literature. The validated models were linked with the deep neural network (DNN) for its training and testing using a total of 6,703 computations with 1,500 iterations. Here, laser power, laser scanning speed and powder feeding rate were selected inputs, whereas porosity was set as an output. Findings The computations indicate that owing to the simultaneous inclusion of powder particulates, the powder elements use a substantial percentage of the laser beam energy for their melting, resulting in laser beam energy attenuation and reducing thermal value at the substrate. The primary operating parameters are directly correlated with the number of layers and total height in CC. Through X-ray computed tomography analyses, the number of layers showed a straightforward correlation with mean sphericity, while a converse relation was identified with the number, mean volume and mean diameter of pores. DNN and analytical models showed 2%–3% and 7%–9% mean absolute deviations, respectively, compared to the experimental results. Originality/value This research provides a unique solution for LMD porosity estimation by linking the developed analytical computational models with artificial neural networking. The presented framework predicts the porosity in the LMD-ed parts efficiently.