## 4 Results and Discussion
### Optimization Results and Verification Test
#### 4.2.2 Supplementary Optimization Experiment  
In a supplementary experiment, spray speed (B), which was not statistically significant in the previous experiments, was excluded. Instead, spray angle (B) was introduced as a new variable [17; 18]. Considering that commercial hand-spray nozzles typically operate within a spray angle range of 40-120\({}^{\circ}\), the dust-spraying device in this study was designed to accommodate spray angles up to 135\({}^{\circ}\). This design configuration enables the analysis of spray angle effects on optimal dust dispersion using a nozzle tip that provides relatively wide coverage. Spray angle, a factor influencing particle diffusion range and surface impact geometry, was set at three levels: 60\({}^{\circ}\), 90\({}^{\circ}\), and 120\({}^{\circ}\). The existing variables, spray pressure (A), spray distance (C), and number of sprays (D), were maintained. However, based on the primary experiment results where spray pressure showed the most significant impact on the response, its range was expanded from the previous 1-3 bar to 1-5 bar. This was intended to explore the curvature effect and optimal pressure conditions more precisely. All variables were combined using FCCD based on RSM and utilized to derive the optimal conditions that maximize the point cloud value. The four factors of the second optimization experiment are presented in Table 7 below. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Spray Pressure** & **Spray Speed** & **Spray Distance** & **Number of Sprays** \\ \hline
3 bar & 100,000 mm/min & 273 mm & 5 counts \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Optimal modeling results. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multirow{2}{*}{**Symbol**} & \multicolumn{4}{c}{**Range of Levels**} \\ \cline{3-5}  & & **Low** & **Center** & **High** \\  & & **(–1)** & **(0)** & **(1)** \\ \hline Spray pressure (bar) & X1 & 1 & 3 & 5 \\ Spray angle (\({}^{\circ}\)) & X2 & 60 & 90 & 120 \\ Spray distance (mm) & X3 & 200 & 300 & 400 \\ Number of sprays (count) & X4 & 1 & 3 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Four factors of the second optimization experiment. Model Adequacy of the Second Optimization Experiment  
Based on the experimental data designed according to FCCD, a basic statistical analysis of the overall model was performed. The results showed an adjusted R-squared value of 76.6%, indicating that the set of independent variables provides adequate explanatory power for the dependent variable, the point cloud value. Furthermore, with an F-value of 7.78 and a _p_-value < 0.0001, it was found that the overall model is statistically significant. Table 8 provides a summary of the ANOVA results for the dust dispersion model. Variable Characteristics Based on Second Optimization Modeling Results  
In the dust-spraying experiment, the regression coefficients for the factors were estimated using the least squares method to ascertain the influence of four factors (A: spray pressure; B: speed; C: spray distance; D: number of sprays) on the point cloud. The resultant second-order polynomial equation is as follows:  
\[ReducedPointCloud=1281.3+129.1A-36.7B+1.81C+29.6D-211.6A2\ -\ 94\text{AD}. \tag{6}\]  
According to Table 9, the final regression model analysis, spray pressure (A) emerged as the variable exerting the most significant influence on the point cloud value. Spray pressure exhibited a statistically highly significant positive (+) main effect, signifying that an increase in pressure contributes to an enhanced density and uniformity of particle distribution on the surface. Conversely, the quadratic term for spray pressure (A\({}^{2}\)) demonstrated a negative (\(-\)) influence, indicating a curvature response where the response value decreases beyond a certain pressure level; this suggests that particle loss or reflection might occur at excessive pressures.