## 4 Simulation Calibration Test
### Calibration Results and Analysis of Different Model Simulations  
Design Expert software was used to conduct a generalized rotating center combination test design. The static friction coefficient and rolling friction factor between wheat particles were selected as the test factors, and the angles of repose for the two measurements were considered evaluation indexes. Thirteen simulation test groups were designed according to the test requirements. After completing the simulation, models with different numbers of filled balls were simulated according to the aforementioned real test process. Post-simulation pictures were exported. To obtain the simulated angle of repose of wheat, MATLAB image processing technology was used to extract simulation pictures and obtain the tangent values of different filled models' angle of repose (Table 9). Figure 5: Image processing under both methods for the angle of repose. \begin{table}
\begin{tabular}{l l l} \hline
**Experiment** & **Lift Test Angle of Repose Tangent** & **Angle of Repose Tangent of the Drawplate Test** \\ \hline
1 & 0.35969 & 0.63162 \\
2 & 0.37113 & 0.64944 \\
3 & 0.32196 & 0.60841 \\
4 & 0.32119 & 0.62062 \\
5 & 0.33241 & 0.63492 \\
6 & 0.32504 & 0.56767 \\
7 & 0.3049 & 0.56909 \\
8 & 0.31307 & 0.55256 \\
9 & 0.30709 & 0.56548 \\
10 & 0.30604 & 0.55845 \\ average value & 0.326 & 0.5958 \\ \hline \end{tabular}
\end{table} 
Table 8: Angle of repose measurements under the two test methods. The analysis of variance (ANOVA) for the simulation test results using Design Expert 8.0.6 software (e.g., Table 10) revealed that both test models were highly significant (\(p<0.01\)), indicating the test's validity. The regression equation for coded values of factors with a good fit and practical analytical significance was derived after eliminating insignificant factors:  
\[Y_{1}=0.3052+0.041A+0.0326B+0.0133 AB+0.0182A^{2}+0.0157B^{2} \tag{3}\]  
\[Y_{2}=0.5658+0.0737A+0.0435B+0.0405 AB+0.0145A^{2}-0.0312B^{2} \tag{4}\]  
Design Expert 8.0.6 software optimized the regression model using constrained objectives and an optimization module so that the simulation results matched the angle of repose of wheat seeds obtained from the experiment as closely as possible. objective function \(\left\{ \begin{aligned} & Y_{1}=0.326\\ & Y_{2}=0.5958\end{aligned} \right.\)  
constraint function \(\left\{ \begin{aligned} &-1.414\leq A\leq 1.414\\ &-1.414\leq B\leq 1.414\end{aligned} \right.\)  
The resulting optimization result was a wheat-wheat static friction factor of 0.0549 and a wheat-wheat rolling friction coefficient of 0.00812. At this time, the angle of repose simulation results met the target indicators. In accordance with the above approach, the other four discrete elemental models of wheat with different filled particle sphere radii \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline \multirow{2}{*}{**Variance Source**} & \multicolumn{2}{c}{\(\mathbf{Y_{1}}\)} & \multicolumn{6}{c}{\(\mathbf{Y_{2}}\)} \\ \cline{2-9}  & **Sum of Squares** & **Freedom** & **F** & **P** & **Sum of Squares** & **Freedom** & **F** & **P** \\ \hline Model & 0.0265 & 7 & 35.78 & 0.0006 & 0.0745 & 7 & 35.78 & 0.0006 \\ A-A & 0.0087 & 1 & 83.55 & 0.0003 & 0.0249 & 1 & 83.55 & 0.0003 \\ B-B & 0.0037 & 1 & 24.19 & 0.0044 & 0.0072 & 1 & 24.19 & 0.0044 \\ AB & 0.0007 & 1 & 22.05 & 0.0054 & 0.0066 & 1 & 22.05 & 0.0054 \\ A\({}^{2}\) & 0.0023 & 1 & 4.94 & 0.0769 & 0.0015 & 1 & 4.94 & 0.0769 \\ B\({}^{2}\) & 0.0017 & 1 & 22.77 & 0.0050 & 0.0068 & 1 & 22.77 & 0.0050 \\ A\({}^{2}\)B & 0.0000 & 1 & 0.0289 & 0.8717 & 8.600E\(-\)06 & 1 & 0.0289 & 0.8717 \\ AB\({}^{2}\) & 0.0003 & 1 & 0.7189 & 0.4352 & 0.0002 & 1 & 0.7189 & 0.4352 \\ Residual & 0.0001 & 5 & & & 0.0015 & 5 & \\ Lack of Fit & 0.0001 & 1 & 0.8200 & 0.4164 & 0.0003 & 1 & 0.8200 & 0.4164 \\ Pure Error & 0.0001 & 4 & & & 0.0012 & 4 & & \\ Cor Total & 0.0266 & 12 & & & 0.0760 & 12 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Analysis of variance.