# Effectiveness of Biomass Pellet Parameters on Their Fractal Dimension
## 4 Results and Discussion
### Influencing Factors on Fractal Parameters of Biomass Pellet  
The results of the data obtained are shown in Table 1.  
Table 1 indicates the actual diameter \(d\) values of the compressed biomass forming pellets under the ring die forming die hole \(d0\) = 6 mm and 8 mm, as well as their corresponding density \(\rho\), surface roughness \(R\)a, and surface hardness HD, while the surface morphology is calculated using the variational method, and the fractal dimension \(D\) values corresponding to the surface morphological characteristics are derived using Equation (10). For \(d0\) = 6 mm, the fractal dimension of the particles ranged from 1.494 to 1.806, but mostly concentrated around 1.6; for \(d0\) = 8 mm, the fractal dimension ranged from 1.430 to 1.914, but mostly concentrated around 1.6, indicating that the fractal dimension of biomass pellets are an isotropic and at the same time self-similar [24; 25]. The data in Table 1 also allow to derive the fractal dimension \(D\) as a function of pellet forming diameter \(d\) (Figure 6), density \(\rho\) (Figure 7), hardness HD (Figure 8), and roughness \(R\)a (Figure 9). Figure 6 Relationship between \(d\) and \(D\). The analysis in Figure 5 shows that the fractal dimension \(D\) tends to decrease as the diameter \(d\) of biomass pellets increases. This is mainly because as the diameter of the formed pellets increases, the surface roughness becomes rougher, and the \(D\) value calculated by the variance method becomes smaller. The reason why the molding diameter \(d\) of wood pellets is larger than the diameter \(d0\) of the forming channel is due to the friction caused to the forming channel by the wood chip materials during the compression molding process. Biomass material comes into periodic contact with protruding parts of the die hole surface or ploughs under cyclic loading, and fatigue spalling of the metal material in this area due to repeated plastic hardening [1]. Thus, the diameter of the die hole becomes larger after wearing, the more serious the forming die hole wear, the diameter of forming pellets also increases. \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{4}{c}{\(d0\) = 6 mm} & \multicolumn{4}{c}{\(d0\) = 8 mm} \\ \cline{2-11}  & \(d\) **(mm)** & \(\rho\) **(g cm\({}^{-3}\))** & \(R\)a (\(\mu\)m)** & **HD** & \(D\) & \(d\) **(mm)** & \(\rho\) **(g cm\({}^{-3}\))** & \(R\)a (\(\mu\)m)** & **HD** & \(D\) \\ \hline
1 & 6.04 & 1.351 & 1.39 & 64.44 & 1.806 & 8.12 & 1.502 & 0.7 & 66.05 & 1.914 \\
2 & 6.08 & 1.304 & 1.25 & 63.2 & 1.82 & 8.26 & 1.483 & 0.9 & 66 & 1.798 \\
3 & 6.11 & 1.298 & 1.47 & 62.73 & 1.649 & 8.32 & 1.452 & 0.94 & 65.29 & 1.664 \\
4 & 6.31 & 1.235 & 2.18 & 63 & 1.69 & 8.37 & 1.398 & 1.05 & 62.02 & 1.672 \\
5 & 6.46 & 1.181 & 2.01 & 60.28 & 1.61 & 8.38 & 1.36 & 1.14 & 60.9 & 1.635 \\
6 & 6.84 & 1.135 & 2.44 & 50.63 & 1.6 & 8.48 & 1.351 & 1.77 & 58 & 1.655 \\
7 & 7 & 1.108 & 2.66 & 43.17 & 1.578 & 8.55 & 1.267 & 1.91 & 56.17 & 1.628 \\
8 & 7.24 & 1.076 & 2.23 & 48 & 1.431 & 8.58 & 1.204 & 2.22 & 55.01 & 1.588 \\
9 & 7.41 & 1.042 & 2.84 & 45.83 & 1.536 & 8.76 & 1.285 & 2.93 & 54.04 & 1.476 \\
10 & 7.65 & 1.025 & 2.99 & 41.2 & 1.494 & 8.98 & 1.269 & 3.31 & 55.03 & 1.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Analysis of influencing factors on fractal parameters of biomass pellet. Figure 5: Surface roughness of the molding particle (\(R\)a = 2.05 \(\mu\)m). From the Figure 7, it can be seen that the fractal dimension \(D\) tends to increase as the density \(\rho\) of biomass pellets increases. This is mainly because the greater the density \(\rho\) of the pellets, the tighter the bonding between the pellets, the better the denseness, and, therefore, the smoother the surface of the pellets, and, therefore, the greater the \(D\) value calculated by the variance method. Figure 8 shows that the fractal dimension \(D\) tends to decrease as the surface roughness parameter \(Ra\) of biomass pellet increases.