# Review on Quality Control Methods in Metal Additive Manufacturing
## 3 Numerical Quality Monitoring Methods in Metal AM and Welding
### Numerical Quality Monitoring Methods in Metal AM  
Several numerical quality monitoring methods in metal AM have focused on identifying the cladding track geometry to predict the dimensional errors of the final products. The cladding track is a trail of the deposited metal. Figure 4 shows a schematic of a single-cladding track. [PERSON] et al. [25] quantified the cross-section of a single-cladding track as a disk shape. [PERSON] et al. [26] proposed a 3D powder-scale multiphysics model with the finite volume method (FVM) to identify the single-cladding track geometry in the DED process. The heat source, powder, and molten pool flow models were included as submodels. Computational fluid dynamics (CFD) was applied to simulate the thermal conditions of a real-scale laser cladding track. The influence of the laser power and DED nozzle speed on the height and width of a single track was numerically quantified using the model. In addition, the authors presented a Gaussian process regression model that can precisely predict the laser cladding track geometry based on the proposed model. [PERSON] et al. [27] proposed a numerical model that considers energy densities to predict the shape of a single-cladding track. The authors observed that a low energy density input to the track caused a large porosity, and a high energy density input produced a wide track. [PERSON] and [PERSON] [28] proposed a numerical model to predict both the height and width of a cladding track in multiple overlapping situations. [PERSON] et al. [29] used a numerical model  
Figure 3: Conceptual representation of (**a**) common anomalies and (**b**) defects in both metal AM and welding. to simulate the multilayer stacking situation of cladding tracks. A finite pointset method (FPM), which has the advantage of less calculation time because the FPM does not generate mesh, was applied to simulate the situation. The model was based on mass, momentum, and energy conservation equations. The relationship between the cladding angle and the temperature distribution of the track was quantified. Additionally, the authors used the model to optimize the laser power to improve the track geometry. The accuracy of the proposed model was validated using a previous finite element method (FEM) model [30]. The authors suggested that the FPM would be a low-cost alternative in the numerical monitoring method for metal AM, compared to the FEM. Various numerical studies have been conducted to identify the causes of residual stress during the metal AM process. Residual stress in a product may result in distortion, fatigue, creep, and corrosion [31]. [PERSON] et al. [32] investigated the major process parameters related to geometrical distortion of PBF products. The distortion and the misalignment of the PBF specimens produced with various parameter settings were evaluated by coordinate-measuring machine (CMM). The authors noted that high thermal gradients could cause thermal residual stress and distortion. Based on both experimental and numerical results, the authors reported that laser path and substrate thickness were the major process parameters for residual stress generation and geometrical distortion. By applying a 3D thermo-mechanical FE model, [PERSON] et al. [33] reported that the complexity of the DED product geometry significantly affected the residual stress generation, and the spiral tool path generated less residual stress when a product had a complex shape. Additionally, the authors reported that the heat input had a significant effect on residual stress generation and distortion, while the powder feeding rate had less effect. Through numerical modeling, [PERSON] et al. [34] simulated the temperature histories of a metal AM product to identify the area under residual stress. The results showed that the deposited area under the stacked layer underwent rapid temperature cycles, which could cause residual stress. The residual stress in the metal AM product was numerically quantified in a study conducted by [PERSON] et al.