## 3 Results and Discussion of RSM Experiments
### Central Composite Response Surface Design  
Based on the results of the steepest ascent test, a central composite design (CCD) under response surface methodology (RSM) was implemented to analyze the interactions among significant parameters [23]. The coded factors and their corresponding levels for the CCD experiments are summarized in Table 9.  
The central composite design (CCD) experimental matrix comprised 14 factorial points, 9 center points for error estimation, and a total of 23 experimental runs. The CCD matrix and corresponding response values (angle of repose) are presented in Table 10, where C\({}^{\prime}\), E\({}^{\prime}\), and G\({}^{\prime}\) represent the coded values of factors C (rolling friction coefficient), E (straw-steel static friction coefficient), and G (JKR surface energy), respectively. The fitting statistics presented in Table 11 indicate that the response surface model achieved a coefficient of determination R\({}^{2}\) = 0.9780, demonstrating strong agreement between the model predictions and experimental data with minimal error. This regression \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Serial**} & \multicolumn{3}{c}{**Factors**} & \multirow{2}{*}{**Stacking**} & \multirow{2}{*}{**Relative**} \\ \cline{2-2} \cline{4-5}  & **C** & **E** & **G** & & **Angle/(\({}^{\circ}\))** & **Error/\%** \\ \hline
1 & 0.14 & 0.43 & 0.01 & 39.20 & 7.32\% \\
2 & 0.17 & 0.45 & 0.03 & 41.5 & 1.89\% \\
3 & 0.20 & 0.47 & 0.05 & 43.80 & 3.55\% \\
4 & 0.23 & 0.49 & 0.07 & 46.1 & 8.98\% \\
5 & 0.26 & 0.51 & 0.09 & 48.3 & 14.18\% \\
6 & 0.29 & 0.53 & 0.11 & 50.6 & 19.62\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Steepest climb test design and results. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Coding**} & \multicolumn{3}{c}{**Factors**} \\ \cline{2-4}  & **C** & **E** & **G** \\ \hline \(-1.68179\) & 0.14 & 0.43 & 0.01 \\ \(-1\) & 0.155 & 0.44 & 0.02 \\
0 & 0.17 & 0.45 & 0.03 \\
1 & 0.185 & 0.46 & 0.04 \\
1.68179 & 0.20 & 0.47 & 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: CCD simulation factor coding table. equation can reliably replace empirical testing for analyzing the relationships between independent variables and the response value. Further validation metrics include an adjusted coefficient of determination \(\text{R}_{\text{adj}}^{2}\) = 0.9628 and a predicted coefficient of determination \(\text{R}_{\text{pre}}^{2}\) = 0.9295. The difference between \(\text{R}_{\text{adj}}^{2}\) and \(\text{R}_{\text{pre}}^{2}\) was less than 0.5, and the coefficient of variation (C.V.) of 0.555% confirmed the model's robustness in reflecting true experimental values. An adequate precision value (signal-to-noise ratio) of 27.3389 (>4.0) further validated the model's excellent fit to the experimental data. Additionally, the rolling friction coefficient between wheat straw particles (C), the static friction coefficient between wheat straw and steel plate (E), the interaction term between rolling friction coefficient and JKR surface energy (C \(\times\) G), the interaction term between static friction coefficient and JKR surface energy (E \(\times\) G), and the quadratic term of JKR surface energy (G2) all exhibited highly significant effects (\(p\) < 0.0001) on the angle of repose of wheat straw feedstock.