## 2 Materials and Methods
### Numerical Calibration
Our objective extended beyond wear minimization, encompassing a holistic examination that included the assessment of structural integrity and mass flow properties. By methodically varying key parameters shown in Figure 5, such as rotational velocity (\(A\), in rpm), clearance (\(B\) in mm), screw diameter (\(C\), in mm), shaft diameter (\(D\), in mm), and Pitch (\(E\) in mm), we studied the effects on structural integrity, power consumption, wear and mass flow. Furthermore, to assess the performance of the screw conveyor, control regions delineated in Figure 5. are used to monitor mass flow during stable material flow. Additionally, a specific geometry region is allocated for the calculation of average shear intensity also during stable material flow. Power consumption is quantified as a consequence of particle interaction along the entire length of the screw conveyor, considering that the material fills the entire length of the housing. Stresses and deformations are analyzed on the screw with the shaft, with total deformation evaluated alongside selected stress points. The DOE framework allowed for a \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Property** & **Unit** & **Value** & **Note/Reference** \\ \hline Geometry: & & & \\ Geometry density \(\rho_{S}\) & [\(kg/m^{3}\)] & 7800 & Structural steel [46] \\ Young’s modulus \(E_{g}\) & [Pa] & 1\(\cdot\)10\({}^{10}\) & Reduced modulus [46] \\ Poisson ratio \(\
u_{g}\) & [–] & 0.3 & Structural steel [46] \\ \hline Particle: & & & \\ \hline Young’s modulus \(E_{p}\) & [Pa] & 2.8\(\cdot\)10\({}^{8}\) & Reduced modulus [40,41] \\ Poisson ratio \(\
u_{p}\) & [–] & 0.4 & Abrasive sand [41] \\ Mean Particle & [\(\mu\)m] & 150 & Measured \\ Diameter \(d_{p}\) & [–] & 18 & Coarse ratio \\ Coarse graining \(c_{gr}\) & [\(kg/m^{3}\)] & 1780 & Measured \\ Bulk density \(\rho_{bulk}\) & [\(kg/m^{3}\)] & 3490 & Calibrated Figure 3 \\ Particle density \(\rho_{p}\) & [\(kg/m^{3}\)] & 3490 & \multicolumn{1}{c}{} \\ \hline Contact: & & & No Slip \\ \hline Hertz Mindlin & & & \\ Sliding friction p-p & [–] & 0.55 & Calibrated Figure 3 \\ \(\mu_{p}\) & & & \\ Sliding friction p-g & [–] & 0.6 & Determined—Inclined plate \\ \(\mu_{g}\) & & & \\ Rolling friction p-p & [–] & 0.1 & Calibrated Figure 3 \\ \(\mu^{r}_{p}\) & & & \\ Rolling friction p-g & [–] & 0.1 & Determined—Inclined plate \\ \(\mu^{r}_{g}\) & & & \\ Coefficient of & & & \\ Restitution & [–] & 0.44 & Assumption based on [41] \\ p-p \(c_{rp}\) & & & \\ Coeficient of & & & \\ Restitution & [–] & 0.50 & Assumption based on [41] \\ p-g \(c_{rg}\) & & & \\ \hline Simulation: & & & \\ \hline DEM Particle count & [–] & 308,609 & - \\ FEM elements count & [–] & 2,138,521 & 4-noded quadratic \\ FEM element size & [mm] & 1.5 & tetrahedral elements \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic obtained material properties and simulation parameters. thorough exploration of the design space, providing insights into the complex relationships between these parameters and their collective influence on the conveyor system. Statistical analyses of the data lead to the identification of optimal design configurations that not only minimize wear but also offer insight into structural integrity and efficient mass flow properties. Throughout this study, the investigation of wear and structural integrity was centred on the screw blade of the screw conveyor, while the other components were neglected based on insights from previous studies [48]. As shown in the process flow in Figure 6, the proposed approach initiates with parametric modelling of a screw conveyor, considering already mentioned key parameters. Geometry can be modelled using parametric modelling software (Solidworks 2022). Once the geometry is parametrically modelled, it is essential to ensure seamless integration with Ansys Workbench geometry modellers by accurately importing the defined parameters.