**1. Introduction**

Interest in laser powder bed fusion (LPBF) additive manufacturing (AM) has spiked in many industries, creating a high demand for new AM-ready metallic materials [1]. However, the mechanical properties, surface finish, and precision of LPBF parts are dependent on more than 60 processing parameters [2], which all need to be optimized. There are currently two main ways to realize this process optimization for new alloys. Most often, this optimization is carried out by defining an experiment plan that covers different arrangements of laser power, scanning speed, hatching space, layer thickness, scanning strategy and part orientation for a given alloy [3–10]. Once the specimens are printed, their mechanical properties are evaluated and a conclusion is drawn on the influence of the different processing parameters on the final part geometric and service attributes. This approach yields satisfying results, but requires multiple printing jobs and time-consuming post-processing experiments. It could easily be realized for a single alloy, but becomes prohibitively expensive if multiple process optimization campaigns are required.

Another way a new AM material can be introduced is by applying a numerical modeling approach with the objective of finding the appropriate printing parameters, as shown in [11–15]. However, due to a large number of variables, these models require significant time and computer resources to model a single laser track, let alone a complex part. Moreover, the more complex the model, the more laborious the calibration procedure, which makes the process optimization more cumbersome and labor-intensive.

In this work, we investigate the possibility of using a combination of a simplified analytical model of the melt pool and of an experimental calibration routine to create a density control algorithm for the laser powder bed fusion process. The main objective of this approach is to reduce the time, the number of printing jobs and the quantity of post-processing characterization work needed to optimize the process for any given powder feedstock and any given LPBF system.

## **2. Methodology**

Previous studies have demonstrated that the density of LPBF manufactured parts is mostly dependent on the following three dimensionless melt pool metrics (Figure 1): melt pool depth-to-layer thickness ratio (*D/t*), melt pool width-to-hatching space ratio (*W/h*), and melt pool length-to-melt pool width ratio (*L/W*), and that the highest density is generally obtained for 1.5 < *D/t* < 2, 1.5 < *W/h* < 2.5 and *L/W* < 2Pi [16,17]. Based on these observations, we investigated the possibility of using the *D/t*, *W/h* and *L/W* ratios to correlate a specific combination of LPBF processing parameters (laser power, scanning speed, layer thickness, and hatching space) with the density of a printed material.

This study was conducted in three phases: first, the analytical model of a thermal field generated by a moving heat source in a solid body is used to evaluate the melt pool dimensions for a given set of LPBF processing parameters. Then, a relationship between the melt pool dimensions and the density of the printed material was found experimentally for a given material and LPBF system. Finally, using the numerical model developed and the experimental relationship found, the LPBF processing parameters were linked to the density of the manufactured parts with the objective of developing a porosity prediction algorithm for different materials and different LPBF systems.

**Figure 1.** Schematic representation of the melt pool and the corresponding geometric characteristics [18].
