## 3 Results and Discussion
### Response Surface  
Contour plots provide valuable visual tools to illustrate the impact of input variables, such as screw blade pitch and screw conveyor angular velocity, on response variables like shear intensity and mass flow. They provide a holistic perspective, allowing engineers to grasp the interconnectedness of various parameters and their effects on system performance. Through the examination of contour plots generated using a fitted model equation, we obtained valuable insights into how variations in these parameters not only influence mass flow, but also influence power consumption, stresses, deformations, and wear in screw conveyors. These plots exposed regions of optimal performance, where various responses were optimized while minimizing undesirable outcomes. The acquisition of such insights is of utmost importance to enhance efficiency in processes involving bulk solids and powders. Furthermore, in the continuation, all parameters that have previously been determined to be significant will be further evaluated through the utilization of response surface analysis, thereby providing a comprehensive understanding of their effects on the system performance. In Figure 12, we present a contour plot illustrating the relationship between mass flow and all input parameters. As clearance increases, mass flow also increases. The material behaved analogous to a threaded nut, with no material left behind on the screw housing. Additionally, we observed that as the screw diameter increases, so does the mass flow. Conversely, an increase in shaft diameter resulted in a decrease in mass flow. Furthermore, we observed that higher pitch values corresponded to higher mass flow rates. These observations highlight the complex relationship between clearance, screw diameter, shaft diameter, and pitch in influencing mass flow dynamics within the system. Similarly, the power needed for driving the screw conveyor demonstrates a rapid increase as clearance decreases and angular velocity increases, as depicted in Figure 13. In addition, the examination of the clearance parameter was conducted to assess its impact on the intensity of shear. This analysis yielded insights into the dissipation of energy during collisions that occurred throughout the simulated period. The quantification of shear intensity, which measures the power transferred per unit area, is of utmost importance in abrasive wear models. \begin{table}
\begin{tabular}{c c c c c} \hline  & **Opti. Function** & **Prediction** & **Simulation** & **Error** \\ \hline Mass flow [t/h] & Target value (5.35) & 5.35 & 5.31 & 0.75\% \\ \hline Shear Intensity [W/m\({}^{2}\)] & Minimum & 14 & 14.56 & 4\% \\ \hline Optimum parameters: & & & & \\ \hline N [rpm] & Clearance [mm] & D\({}_{\text{screw}}\) [mm] & D\({}_{\text{shaf}}\) [mm] & Pitch [mm] \\ \hline
167 & 8.60 & 80 & 27 & 87 \\ \hline \end{tabular}
\end{table} 
Table 4: Response optimization data with the comparison of predicted and simulated results. It facilitates the determination of shear wear on geometric surfaces and directly demonstrates wear rates. The shown trend in Figure 14 (right) illustrates an increase in throughput performance with higher angular velocity and reduced clearance. Consequently, this leads to higher wear rates in the screw model. Similarly to the findings in [42], where the vertical screw conveyor was studied we can compare the relationship between the rotation speed and the wear rate of the screw flight. We noted that with the increase in rotation speed, the trend of the wear rate increases, confirming the reported observations. Similarly to the findings, our study also observed that the most severe wear occurs at the outer edge of the screw blade. Interestingly, we found that the amount of wear on the inner side of the screw shaft is relatively small, aligning with the observations. Figure 12: Parametric Mapping of Mass Flow Dynamics in [t/h]: Contour Analysis Across Pitch, Angular Velocity, Shaft Diameter, Screw Diameter, and Clearance with Hold Values from Response Optimization.