## 2 Materials and Methods
### Numerical Calibration
The primary workflow is subsequently transferred to Ansys Workbench, where seamless integration facilitates automatic instances between Ansys Rocky (DEM) and Ansys Transient Structural (FEM) modules. Within the Workbench environment, the simulation procedure is automated, streamlining the analysis process and ensuring efficient execution of the coupled DEM/FEM simulations. Within the framework of discrete element analysis, angular velocity is systematically varied, leading to the extraction of crucial data such as shear intensity and wear displacement from the simulation results. The process begins with an empty screw conveyor. With free-flowing material from the hopper typically horizontal screw conveyors operate with a recommended filling rate of around 40% of the screw channel cross-section which refers to the shape or profile of the internal cavity within the screw conveyor through which material is transported. However, due to the short length (1000 mm) and the absence of additional barriers like bearing holders, the filling rate was not controlled in this study. Sufficient material was present to fill the screw conveyor, and the simulation proceeded until the material exited the bounding box. The analysis extends to the ANSYS Transient module, where, for each timestep defined by the DEM outputs frequency, stresses and deformations are calculated. This iterative procedure is fully automated and continues until all designated design points have undergone evaluation. In DEM, material calibration via real experiments refined model accuracy, with validated mass flow calculations from standard [17] aligning well with simulations. Figure 5: Key Parameters and Control Regions for the Screw Conveyor System. The figure illustrates essential study parameters including rotational velocity (A, in rpm), clearance (B, in mm), screw diameter (C, in mm), shaft diameter (D, in mm), and Pitch (E, in mm), alongside delineated control regions. FEM simulations underwent validation, including Ansys coupling and convergence analyses, supported by custom simulations. The final step involves creating a response surface chart, which visualizes how various variables interact with each other. This step is crucial for optimization. Before this, response surface results are collected and exported to Minitab for regression analysis, complemented by a thorough optimization run aimed at refining and improving the overall performance of the screw conveyor design. When applying the Discrete Element Method (DEM) for numerical simulations, particularly in the optimization of conveying processes, the utilization of the Response Surface Method (RSM) offers various advantages. First, RSM enables the design of a minimal number of simulation runs, thereby enhancing the efficiency of computational time and resources. Figure 6: Flowchart of the Proposed Approach for Screw Conveyor Design Optimization. Additionally, DEM simulations provide a profound understanding of intricate particle interactions during powder conveying, and RSM analysis further enhances comprehension by clarifying how variations in input parameters impact output responses, thereby assisting in the optimization of simulation parameters and maximizing efficiency while minimizing wear. Moreover, RSM enables the iterative refinement of DEM models based on predictions, leading to continuous improvement of predictive capabilities. Central Composite Design (CCD) proves to be a powerful experimental approach to strategically situating points within a design space, enabling researchers to effectively investigate complex systems. CCD's distinctive configuration of the centre, axis, and factorial points allows for the in-depth study of main effects, interaction effects, and curvature. Its adaptability benefits through design variations such as Face-Centered and Rotatable, adjusting experiments to specific objectives.